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Chapter 8: Q. 41 (page 535)

In the given problem solve the triangle using either the law of sines or law of cosines-

b=5,c=12,A=60掳

Short Answer

Expert verified

Required values of the triangle are

a=10.44,B=13.8掳,C=34.75掳

Step by step solution

01

Step 1. Given information

In the given triangle,

b=5,c=12,A=60掳

We know Law of cosines,

a2=b2+c2-2bccosA -------1

Also, Law of sines,

sinAa=sinBb=sinCc -------2

02

Step 2. Calculation

For a, using equation 1

a2=b2+c2-2bccosA鈬�a2=52+122-2脳5脳12.cos60掳鈬�a2=25+144-120脳0.5鈬�a2=109鈬�a=10.44

For B, using equation 2

sinAa=sinBb鈬�sin60掳10.44=sinB5鈬�0.510.44=sinB5鈬�sinB=0.239鈬�B=sin-10.239鈬�B=13.8掳

For C, using equation 2

sinAa=sinCc鈬�sin60掳10.44=sinC12鈬�sinC=0.5脳1210.44鈬�sinC=0.57鈬�C=sin-10.57鈬�C=34.75掳

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Most popular questions from this chapter

What do you do first if you are asked to solve a triangle and are given one side and two angles?

Solve each triangle.

a=4,b=5,c=3

Write the formula for the distance dfrom P1=x1,y1to P2=x2,y2.

Find the distance from A to C across the gorge illustrated in the figure.

Find the area of the triangle. Round answer to two decimal places.

B=70掳,C=10掳,b=5
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