Question

In ΔNOP, the measure of ∠P=90°, PN = 95 feet, and OP = 31 feet. Find the measure of ∠O to the nearest degree.

Answer 1

Given:

In ΔNOP, the measure of ∠P=90°, PN = 95 feet, and OP = 31 feet.

To find:

The measure of ∠O to the nearest degree.

Solution:

In a right angle triangle,

$\tan \theta=\dfrac{Opposite}{Adjacent}$

In triangle NOP,

$\tan O=\dfrac{PN}{OP}$

$\tan O=\dfrac{95}{31}$

$O=tan^{-1}\dfrac{95}{31}$

$O=71.92768$

$O\approx 72$

Therefore, the measure of angle O is 72 degrees.