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____ [38]
3 years ago
7

3. braay enjoys spending money at the hardware store. He gets along wonderfully with the owner. He

Mathematics
1 answer:
Lorico [155]3 years ago
8 0

Answer:

brady will get 58.14 dollars back

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Answer:

Part A 1 solution

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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
jek_recluse [69]

Answer:

\displaystyle \cos(A + B) =\frac{969}{1769}

Step-by-step explanation:

We are given that:

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

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:

o=\sqrt{29^2-20^2}=21

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

h=\sqrt{11^2+60^2}=61

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:

\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B

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:

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

Simplify:

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

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<span>I just worked out the problem , the answer should be ....


2,304 π cubic units
 

Hope this helps.</span>
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Check the picture below.

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