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Chapter 8: Q. 31 (page 541)

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

A=110°,C=30°,c=3

Short Answer

Expert verified

The area of the triangle is 5.44 square units.

Step by step solution

01

Step 1. Given information.

The given values are:

A=110°C=30°c=3

02

Step 2. Determine the third angle.

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

A+B+C=180°110°+B+30°=180°B=180°-140°B=40°

03

Step 3. Determine the area of the triangle.

The area of a triangle is:

K=c2sinAsinB2sinC

Substitute the values in the above formula.

K=(3)2sin(110°)sin(40°)2sin(30°)K=9(0.9397)(0.6429)2(0.5)K=5.4371...K≈5.44

04

Step 4. Conclusion.

The area of the triangle is 5.44 square units.

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