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Bingel [31]
3 years ago
6

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

.
Mathematics
1 answer:
jek_recluse [69]3 years ago
3 0

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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Step-by-step explanation:

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3.73 hours

Explanation:

In 1 hour, Lisa does 1/7th of the order while Bill does 1/8th of the order in an hour. To find out how long it will take them to fill the order, we have to:

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Add the rate of both Lisa and Bill together

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Step 2:

Since both denominators of the fractions are different, you have to find the least common multiple of 7 and 8

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Step 3:

Then, you have to multiply the numerator of 1/7 with 8 and the numerator of 1/8 with 7.

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The fractions would now have equal denominators:

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Step 4:

Now, you can add them together

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