Chapter 8.3, Problem 5AYU

If two sides and the included angle of a triangle are given, which law can be used to solve the triangle?

a. Law of Sines

b. Law of Cosines

c. Either a or b

d. The triangle cannot be solved.

To determine

To find: Which of the given option is correct.

Answer to Problem 5AYU

Solution:

$b$

Explanation of Solution

Given:

If two sides and the included angle of a triangle are given, which law can be used to solve the triangle?

a. Law of Sines   b. Law of Cosines   c. Either $\text{a}$ or $\text{b}$   d. The triangle cannot be solved.

Calculation:

When 2 sides and included angle of a triangle are given, we can use Law of cosine to solve the triangle.

2 sides and included angle of a triangle means, either $a, b, C$ or $b, c, A$ or $c, a, B$ will be given and we can use Law of cosine to solve the triangle.

The cosine formulae are given below.

$\text{Cos}A = \frac{b^2 + c^2 - a^2}{2bc}$

$\text{Cos}B = \frac{a^2 + c^2 - b^2}{2ac}$

$\text{Cos}C = \frac{b^2 + a^2 - c^2}{2ab}$

Hence option $\text{b}$ is correct.