Question

This problem refers to triangle ABC. If b = 3.5 m, c = 7.2 m, and A = 114°, find a. (Round your answer to one decimal place.) a = ? m

Answer 1

To find side a of triangle ABC, we can use the law of cosines, which states that:

a² = b² + c² - 2bc cos(A)

Substituting the given values, we get:

a² = 3.5² + 7.2² - 2(3.5)(7.2)cos(114°)

Simplifying, we get:

a² = 12.25 + 51.84 - 50.4(-0.3917)

a² = 12.25 + 51.84 + 19.77

a² = 83.86

Taking the square root of both sides, we get:

a ≈ 9.2

Therefore, side a of triangle ABC is approximately 9.2 meters.