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:
[tex]\cos\angle C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where,
a = 12 ft
b = 5 ft
c = 10 ft
∠C = ∠P
Substitute into formula
[tex]\cos\angle P=\dfrac{12^2+5^2-10^2}{2\cdot 12\cdot 5}[/tex]
[tex]\cos \angle P=0.575[/tex]
[tex]\angle P=\cos^{-1}0.575[/tex]
[tex]\angle P=54.9\approx 55^\circ[/tex]
Hence, The ∠P is equal to 55°
