Question

What is the measure of ∠P, to the nearest degree? 24° 42° 55° 101°

Answer 1

Answer:

The ∠P is equal to 55°

Step-by-step explanation:

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

Using cosine law:

$\cos\angle C=\dfrac{a^2+b^2-c^2}{2ab}$

where,  

a = 12 ft

b = 5 ft

c = 10 ft

∠C = ∠P

Substitute into formula

$\cos\angle P=\dfrac{12^2+5^2-10^2}{2\cdot 12\cdot 5}$

$\cos \angle P=0.575$

$\angle P=\cos^{-1}0.575$

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

Hence, The ∠P is equal to 55°

Answer 2

I used cosine law and I got : 55°