Question

If m∠B = 13°, a = 15, and c = 21, what are the measures of the remaining side and angles? Group of answer choices m∠A = 20.3°, m∠C = 146.7°, b = 7.2 m∠A = 27.9°, m∠C = 139.1°, b = 7.2 m∠A = 20.3°, m∠C = 146.7°, b = 9.7 m∠A = 27.9°, m∠C = 139.1°, b = 9.7

Answer 1

The solution of the triangle is b = 7.2 m∠A = 27.9°, m∠C = 139.1°. Option C

How to solve a triangle?

Solving a triangle involves finding the unknown side lengths and angle measures of a triangle given some of its known elements. The methods to solve a triangle depend on the information provided.

We know that;

`b^2` =
`a^2`+
`c^2` - 2acCosB

`b^2` =
`(15)^2`+
`(21)^2` - 2 * 15 * 21 Cos 13

b = √
`(15)^2`+
`(21)^2` - 2 * 15 * 21 Cos 13

b = √666 - 614

b = 7.2

Given that;

a/Sin A = b/SinB

15/Sin A = 7.2/Sin 13

A = Sin-1 (15 Sin13)/7.2

= 27.9 degrees

C = 180 - (13 + 27.9)

= 139.1 degrees