Chapter 8.4, Problem 4AYU

True or False The area of a triangle equals one-half the product of the lengths of two of its sides times the sine of their included angle.

To determine

To find: Whether the given statement is true or false: The area of a triangle equals one–half the product of the lengths of two of its sides times the sine of their included angle.

Answer to Problem 4AYU

Solution:

True.

Explanation of Solution

Given:

The area of a triangle equals one–half the product of the lengths of two of its sides times the sine of their included angle.

Calculation:

If two sides $\text{a}$ and $\text{b}$ and the included angle $\text{C}$ are known in a triangle, then the area $\text{K}$ is found using the formula $K = \frac{1}{2} ab\text{sin}C$

Hence, the statement “The area of a triangle equals one–half the product of the lengths of two of its sides times the sine of their included angle” is true.