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Alexxx [7]
2 years ago
13

For positive acute angles A and B, it is know that tan A= 8/15 and sin B= 11/61. Find the value of cos (a+b) in simplest form

Mathematics
1 answer:
iragen [17]2 years ago
7 0

Answer:

812/1037

Step-by-step explanation:

To solve this, we have to use trigonometric identities.

Cos (A + B) is given as Cos A Cos B - Sin A Sin B. And from the question, we have that

Tan A = 8/15.

We know that in a triangle, the Tan angle is represented Opp/Adj and thus the Opp is 8, and the Adj is 15. Using Pythagoras, we have

hyp² = opp² + adj²

hyp² = 8² + 15²

hyp² = 64 + 225

hyp² = 289

hyp = √289 = 17

The identity of Cos is Adj/Hyp and that of Sin is Opp/Hyp.

Cos A = 15/17

Sin A = 8/17

Repeating the same process for B, we have

Sin B = 11/61

adj² = hyp² - opp²

adj² = 61² - 11²

adj² = 3721 - 121

adj² = 3600

adj = √3600 = 60

Cos B = 60/61

Now, using the earlier stated trigonometric identity, we have

cos (a + b) = CosA CosB - SinA SinB

cos (a + b) = 15/17 * 60/61 - 8/17 * 11/61

cos (a + b) = 900/1037 - 88/1037

cos (a + b) = 812/1037

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Priya is hosting a poetry club meeting this week and plans to have fruit punch and cheese for the meeting. She is preparing 8 ou
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Answer:

i) Number of people in club = 12

ii) 96 ounces of fruit punch for 12people

iii) 24 ounces of cheese for 12 people

iv) Priya's budget for poetry club meeting in dollars = $7.87

Step-by-step explanation:

We are not given the options for the equations that could represent the quantities and constraints in this situation. We can tell we are to represent the information given above.

Number of people in the club = 12

8 ounces of fruit punch per person

For 12 people = 12×8 = 96 ounces of fruit punch

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For 12 people = 12×2 = 24 ounces of cheese

A package of cheese = 16 ounces

The costs for 1package = $3.99

The costs for 16 ounces of cheese = $3.99

The cost for 24 ounces of cheese = (24×3.99)/16 = 5.985

The cost for 24 ounces of cheese = $5.99

One-gallon jug of fruit punch = 128 ounces

The cost of One-gallon jug of fruit punch = $2.50

The costs of 128 ounces of fruit punch = $2.50

The costs for 96 ounces of fruit punch = (96×2.5)/128 = 1.875

The costs for 96 ounces of fruit punch = $1.88

Priya's budget for poetry club meeting in dollars = $5.99 + $1.88 = $7.87

Cost per item for x number of people:

y = x(2.5/128) + x (3.99/16)

y = x(0.0195) + x(0.2494)

Cost equation for Priya's budget:

y = 96x(2.5/128) + 24x (3.99/16)

y = 96x(0.0195) + 24x(0.2494)

Since the total number of people to attend the meeting is 12, the constraint = 0≤x≤12

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