Question

A piece of wire is bent into the shape of a triangle. Two sides have length 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Answer 1

The length of the third side is approximately ≈ 14.79 inches

Explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2 = a^2 + b^2 - 2ab cos C

c = √a^2 + b^2 - 2ab cos C

c = √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately 14.79 inches.

Hope this helps!