Question

A triangular lawn has sides that are 8 m and 12 m long with an included angle of 49°.

What is the area of the lawn?

Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth

Answer 1

Area ≈ 41.4 square meters

Explanation:

We can use the formula for the area of a triangle given two sides and the included angle between them:

Area = (1/2)ab sin(C)

where a and b are the lengths of the two sides and C is the included angle between them.

In this case, a = 8 m, b = 12 m, and C = 49°. We can convert the angle to radians by multiplying by π/180:

C = 49° × π/180 = 0.855 radians

Substituting into the formula, we get:

Area = (1/2)(8 m)(12 m) sin(0.855)

Area ≈ 41.4 square meters

Therefore, the area of the lawn is approximately 41.4 square meters.