Question

In triangle XYZ, side x is 38 units, side y is 19 units, and the measure of angle Z is 51˚. What is the area of triangle XYZ?

Question 4 options:

483.9 square units


280.5 square units


242.0 square units


561.1 square units

Answer 1

242.0 square units

Explanation:

For a triangle ABC whose lengths are a, b and c with the sides facing the angles A, B and C respectively, then the area T of the triangle may be expressed as

T = 1/2 ab Sin C

T = 1/2 bc Sin A

T = 1/2 ac Sin B

depending on the angle and sides given.

Hence for the given triangle, the area

= 1/2 * 38 * 19 * Sin 51˚

= 361 * 0.6702

= 241.94 square units

≈ 242.0 square units