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=(Opposite)/(Adjacent)`

In triangle NOP,

`\tan O=(PN)/(OP)`

`\tan O=(95)/(31)`

`O=tan^(-1)(95)/(31)`

`O=71.92768`

`O\approx 72`

Therefore, the measure of angle O is 72 degrees.