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How can I solve this question using trigonometry

How can I solve this question using trigonometry-example-1
User Kerrin
by
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2 Answers

3 votes

Answer:


(pr)/( \sin(q) ) = (rq)/( \sin(p) ) = (pq)/( \sin(r) )

User Mikegross
by
7.6k points
2 votes

Answer:

a) R = 47.28 R = 312.73 b) 6.67

Explanation:

a)

Use the sine rule to calculate angle PRQ


(sinQ)/(q) = (sinR)/(r)


(sin40)/(7) = (sinR)/(8)


0.091827 = (sinR)/(8)


sinR = 0.73461


sininverse(0.73461) = R


R = 47.28

2nd angle for PRQ is 360 - 47.28 = 312.73

b) Use the cosine rule to find side p

p² = r² + q² - 2rqcosP

To find the angle of p we will simply subtract angle R and angle Q from 180.

180 - 47.28 - 40 = 92.72

p² = 8² + 7² + 2(8)(7)cos(92.72)

p² = 107.685

p = √107.685

p = 10.38

Let's suppose that the shortest distance of R from PQ is
x.

look at the diagram I gave

since the line I made makes a right angled triangle, we can use SOH CAH TOA

for the angle 40,
x is opposite and 10.38 is hypotenuse

which means we will have to use SOH

sin40 = O/H

sin40 =
x\\/10.38

0.6428 =
x/10.38

0.6428 × 10.38 =
x


x = 6.67

How can I solve this question using trigonometry-example-1
User Yewande
by
7.5k points

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