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Chapter 8: Q. 25 (page 541)

Area of an ASA Triangle If two angles and the included side are given, the third angle is easy to find. Use the Law of Sines to show that the area K of the triangle with side aand angles A, B, and C is

K=a2sinBsinC2sinA

Short Answer

Expert verified

The area of the triangle isK=a2sinBsinC2sinA.

Step by step solution

01

Step 1. Given information.

The angles of a triangle are A, B and C.

The side of the triangle is a.

The area of the triangle is K.

02

Step 2. Determine the another side.

According to the Law of Sines:

asinA=bsinB=csinC

Using the Law of Sines, we get

asinA=bsinBasinBsinA=b

03

Step 3. Prove the given statement.

If two sides a,band included angle Cis given, then the area of the triangle is:

K=12absinC

Substitute the value of b.

K=12aasinBsinAsinCK=a2sinBsinC2sinA

Hence proved.

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