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Chapter 13: Q. 12 (page 870)

Solve the following triangle and determine its area.

Short Answer

Expert verified

The value of side:a=6

m鈭�B=33om鈭�C=90o

Step by step solution

01

Step 1. Given information.

Triangle is :

02

Step 2. Apply cosine formula to the triangle and find a.

cos(40o)=52+92-a22脳5脳9cos(40o)=25+81-a290106-a2=90cos(40o)106-a2鈮�69a2鈮�106-69a鈮�37a鈮�6

03

Step 3. Apply sine formula to the triangle.

sin40o6=sinB5=sinC9

By taking first two fractions,

sin40o6=sinB5sinB=5sin40o6sinB鈮�3.216sinB鈮�0.53B鈮�33o

By taking first and last fraction,

sin40o6=sinC9sinC=9sin40o6sinC鈮�1C=90o

04

Step 4. To find the area of the triangle.

A=s(s-a)(s-b)(s-c)

s=a+b+c2s=6+5+92s=10

A=10(10-6)(10-5)(10-9)A=10(4)(5)(1)A=200A=102A鈮�14.14

So the area of the triangle is approximately 14.14 square units.

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Most popular questions from this chapter

List all the combinations of 5 objects a,b,c,d, and etaken 3 at a time. What isC(5,3)?

C(n,r)=______

A(n) _____________ is an ordered arrangement of robjects chosen from nobjects.

IfnA=15,nB=20,nA鈭�B=10. findnA鈭�B.

Use the formula C(n,r)=n!(n-r)!r!to find the value of each combination.

C(18,1)
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