For positive acute angles A and B, it is known that cos A= 20/29 and tan B= 11/60. Find the value of cos(A + B) in simplest form.

Answers

Answer 1

Answer:

[tex]\displaystyle \cos(A + B) =\frac{969}{1769}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}[/tex]

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

[tex]o=\sqrt{29^2-20^2}=21[/tex]

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

[tex]h=\sqrt{11^2+60^2}=61[/tex]

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

[tex]\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B[/tex]

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

[tex]\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)[/tex]

Simplify:

[tex]\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}[/tex]


Related Questions

Peter, Bridget and Caroline share some sweets in the ratio 2:5:2. Peter gets 14 sweets. How many did Bridget get?

Answers

Answer:

35

Step-by-step explanation:

The 14 sweets Peter gets is 2 parts of the ratio, then

14 ÷ 2 = 7 ← number of sweets in 1 part of the ratio , then

5 parts = 5 × 7 = 35 ← number of sweets Bridget gets

Jorge got a hit 8/25 of the times that he
batted. What percent of the times did
he get a hit?

Answers

Answer:

32%

Step-by-step explanation:

Percent means out of 100 so we need the denominator to be 100

8/25  * 4/4 = 32/100

The percent is the numerator since it is now out of 100

32%

Answer: 32%

Step-by-step explanation:

32%

what is the value of x

Answers

Answer:

20

Step-by-step explanation:

Those angles are the same so you can put them in an equation like this:

x + 60 = 4x

Then you subtract x from both sides to get variables on one side and constants on the other:

60 = 3x

Now divide by three to find what just x is:

20 = x

And there you go <3

Write a division equation and solve (Hint: write the mixed number as an improper fraction): If the host intends to serve each guest at the party 1/5 of a pizza, how many servings can be made with the remaining 2 1/2 pizzas?

Answers

Answer:

Step-by-step explanation:

fraction of pizza=5/2

host serves to each guest=1/5*5/2

=5/10

so no of serving that can be done with the remaining 21/2 pizza

5/10-1/5

5*1-1*2/10

5-2/10

3/10

Find m1 please help will give brainlyest

Answers

Answer:

The intercepted arc is twice the value of the inscribed angle. Since the intercepted arc is 110°, this means that the inscribed angle 1 is 55°.

1 = 55 degrees
Explanation it is

Convert the measurement as indicated

12 yd to foot



Show steps



Will give Brainlist



Help

Answers

Answer:

36 ft

Step-by-step explanation:

Given :

12 yards.

We need to convert it into feets. We know that ,

[tex] \implies[/tex] 1 yard = 3 feet

[tex] \implies[/tex] 12 yards = 12 * 3 ft

[tex] \implies[/tex] 12 yards = 36 ft .

Hence the required answer is 36 feets .

Answer:

the formula for converting yards into feet: 1 yard is equal to 3 feet. Write out the necessary math problem or use a calculator. If you want to convert 21 yards, for example, the problem would be 21 multiplied by 3 (21 x 3). Finish the conversion.

SO,

12 yd 36.00 ft

Will give brainliest

The ages of two groups of karate students are shown in the following dot plots:


A dot plot shows Age in years on the horizontal axis. For Group A, there are 2 dots on 4, 5 dots on 5, 3 dots on 7, 4 dots on 8, 2 dots on 9, 2 dots on 11, and 1 dot on 14. For Group B, there is 1 dot on 7, 2 dots on 8, 1 dot on 9, 1 dot on 11, 1 dot on 16, 2 dots on 19, 2 dots on 20, 2 dots on 21, and 1 dot on 26.


The mean absolute deviation (MAD) for group A is 2.07 and the MAD for group B is 5.51. Which of the following observations can be made using these data?


Group A has greater variability in the data.

Group A has less variability in the data.

Group B has a lower range.

Group B has a lower mean.

Answers

Answer:

Group A has greater variability in the data.

Step-by-step explanation:

We use elimination. Clearly, from the MAD, Group A has greater variability in the data.

So, choice 1.

PLEASE HELP!!
What is x? Show your work.

Answers

Answer:

Girl i dont know im so sorry

Step-by-step explanation:

good luck on ur assignment tho xoxo

The average distance between the planet Neptune and the sun is about 4 x 10^9 kilometers. What is 4 x 10^9 written in standard notation?

A. 0.0000000004
B. 0.000000004
C. 400,000,000
D. 4,000,000,000

Answers

D. 4,000,000,000

The 9 shows that the decimal moves to the right 9 times. If it were a -9 it would move to the left 9 times.

PLEASE HELP ASAP :D
what is
sin
cos
tan

Answers

Answer:

sin=180/181

cos=19/181

tan=19/180

What is the standard equation of a circle with center (-2,0) and radius 4?

Answers

Answer:

B(x+2)^2+y^2=16

Step-by-step explanation:

since you have an x-coordinate only and it is negative and a y coordinate which is 0..basically x will appear positive with its conjecture x^2 and the y value will be independent...y^2...bare in Mind that radius is always squared hence it is 16 instead of 4

When did the low temperature occur?
A 0 midnight
B 3 am
C 5 am
D 15(3PM)

Answers

Answer:C

Step-by-step explanation:

We can see that at 5 am it is at the lowest point.

Answer:

C 5am

Step-by-step explanation:

The temperature starts at midnight which is 35. But if you look at the bottom of the chart there is a 5am, 10am, 15(3pm). At 5am it went down to 30. And then went back up.

A set of pythagorean triples is: ____

A. 12, 16, 20
B. 8, 12, 16,
C. 3, 5, 9,
D. 1, 1, 2

Answers

A

Used Pythagorean theorem

Given the vertices of a triangle ABC below, find the midpoint and length of the midsegment. Give your length in simplified radical form.

Answers

Answer:

Midpoint of AC = (-1, 1)

Midpoint of BC = (1, -2)

Length of the midsegment = [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Vertices of a triangle ABC are A(0, 5), B(4, -1) and C(-2, -3).

Midpoint of segment AC = [tex]\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]

                                         = [tex](\frac{0-2}{2},\frac{5-3}{2})[/tex]

                                         = (-1, 1)

Midpoint of BC = [tex](\frac{4-2}{2},\frac{-1-3}{2})[/tex]

                         = [tex](1,-2)[/tex]

Length of the mid segment = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                              = [tex]\sqrt{(-1-1)^2+(-2-1)^2}[/tex]

                                              = [tex]\sqrt{4+9}[/tex]

                                              = [tex]\sqrt{13}[/tex]

Find the missing measurements.

Area: ?

Length: 13 cm

Width: 15 cm

Answers

Answer:

13 x 15 = 195

The topic is about secant tangent angles

Answers

Answer:

x = 71

Step-by-step explanation:

The chord- chord angle is half the sum of the arcs intercepted by the angle and its vertical angle, that is

x = [tex]\frac{1}{2}[/tex] (92 + 50) = 0.5 × 142 = 71

Wants to wrap a shipping box shaped like a rectangular prism. The box is 25 inches tall and has a square base with sides that each measure 6 inches. How much paper will she​ use?

Answers

Answer:

672 square inches

Step-by-step explanation:

Given data

Height= 25inches

Lenght = 6 inches

Width= 6 inches

The expression for the area of the box is given as

TSA= 2 (lh + lw+ hw)

TSA= 2(6*25+ 6*6+ 25*6)

TSA=  2(150+ 36+150 )

TSA= 2*(336)

TSA= 672 square inches

The function f(x)=-\x-4/+6 is increasing
through the interval -
A. 6 C. 4 B. -00< x < 4
D. 4 :)

Answers

Answer:

Option B

Step-by-step explanation:

Given function is,

f(x) = -|x - 4| + 6

By using a graphing tool we can get the graph of the given function.

From the graph attached slope of the line drawn from [tex]x=-\infty[/tex] to [tex]x=4[/tex] is positive while slope of the line from [tex]x=4[/tex] to [tex]x=\infty[/tex] is negative.

Therefore, segment showing a positive slope will be increasing in the given interval [tex]-\infty<x<4[/tex].

Function 'f' is increasing in the interval [tex]-\infty<x<4[/tex].

Option B will be the correct option.

I need help with this please.

Answers

From the options I see it would be -1

HELP NOW PLEASE I HAVE 10 MINUTES! 20 POINTS
If f(x) = 4x^2 + 1 and g(x) =x^2 - 5, find (f-g)(x)

Me and my procrastination habits smh
Also let me know if you can help with other questions I have 2 more

Answers

Slope:  

2

3

y-intercept: (0,−6)xy0−63−4

i’m pretty sure the answer is 3x^2+6

let me know if this doesn’t make sense and i can fix it :)

The diameter of a cylindrical construction pipe is 4ft . If the pipe is 24ft long, what is its volume

Answers

If you need the answer using pi it’s also there

Using the function p(x)=4x-3 what is p(5)

Answers

Answer:

p(5) = 17

Step-by-step explanation:

p(x) = 4x - 3

p(5) = 4(5) - 3

     = 20 - 3

     = 17

What is the est. decimal for the square root of 50?

Answers

Answer:

7.071

Step-by-step explanation:

Hope this helps

The answer to your question would be 7.0
The estimated decimal square root of 50.0 is 7.0.

Hope this helped,

Have a great afternoon.

Subtract 4.25 and 12.835​

Answers

Answer:

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

[tex]12.835 - 4.25 \\ = 12.835 - 4.250 \\ = 8.585[/tex]

NOTE:-

You must subtract the smaller number from the bigger number.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

Rewrite the expression in the form zn.

Answers

Answer:

zⁿ = z³

Step-by-step explanation:

We have the expression:

√(z/ z^⅓)

Hence

= z^½/ (z^⅓)^½

= z^½/ (z^⅙)

= z^(½ ÷⅙)

= z ^(1/2 × 6/1)

= z³

Therefore: zⁿ = z³

Length of rectangle is 2(7z + 3) meters. the width is 5z meters than length perimeter in terms of z please

Answers

Answer:

Step-by-step explanation:

Given,

Length (l) = 2(7z + 3) = 14z + 6

Breadth (b) = 5z

Now,

Perimeter of rectangle (P) = 2(l + b)

                                           =2(14z + 6 + 5z)

                                           =2(19z + 6)

                                           =38z + 12

1. True or False
3 € {1, 2, 3, 4, 5}
True
O False

Answers

the anwser for this is true

Answer:

I also think it's true because it mostly made sense to me.

thr value of k if x-1 is a factor of 2x^3 +3 kx^2+2x-1​

Answers

Answer:

-2/3

Step-by-step explanation:

put 1 in x should be 0

k is -2/3

You are hiking in Marin, and stop to stand on the edge of a cliff overlooking the Pacific ocean. You see a sailboat down in the water below you. The angle of depression to the sailboat is 28◦ . A quick tells you that the cliff you’re standing on is 150ft. How far away from the boat are you, in feet, rounded to one decimal place?(30pts)

Answers

Answer:

Step-by-step explanation:

on the edge of a cliff overlooking the Pacific ocean. You see a sailboat down in the water below you. The angle of depression to the sailboat is 28◦ . A quick tells you that the cliff you’re standing on is 150ft. How far away from the boat are you, in feet, rounded to one decimal place?(30pts)

We solve using the Trigonometric function of TANGENT

tan 28 = 150/x

Which of the following formulas is used to find the circumference of a circle?
O A. C = op?
B. C = 23d
O C. C = 8012
O D. C = 281

helpp someoneee

Answers

Answer:

D.

Step-by-step explanation:

Circumference of a circle is also referred to as the perimeter bordering the circle.

Thus, it is given as:

C = 2πr

C is circumference

r = half of the diameter of the circle = r

This formula used in finding the circumference of a circle is C = 2πr

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