Question

What is the measure of ∠P, to the nearest degree?

24°

42°

55°

101°

Answer 1

I used cosine law and I got : 55°

Answer 2

The ∠P is equal to 55°

Explanation:

We are given three sides of triangle and to calculate the one angle of corresponding to 10 ft side.

Using cosine law:

`\cos\angle C=(a^2+b^2-c^2)/(2ab)`

where,

a = 12 ft

b = 5 ft

c = 10 ft

∠C = ∠P

Substitute into formula

`\cos\angle P=(12^2+5^2-10^2)/(2\cdot 12\cdot 5)`

`\cos \angle P=0.575`

`\angle P=\cos^(-1)0.575`

`\angle P=54.9\approx 55^\circ`

Hence, The ∠P is equal to 55°