angelicaaguilar77 angelicaaguilar77
  • 17-03-2021
  • Mathematics
contestada

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

Respuesta :

erinna erinna
  • 22-03-2021

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,

[tex]\tan \theta=\dfrac{Opposite}{Adjacent}[/tex]

In triangle NOP,

[tex]\tan O=\dfrac{PN}{OP}[/tex]

[tex]\tan O=\dfrac{95}{31}[/tex]

[tex]O=tan^{-1}\dfrac{95}{31}[/tex]

[tex]O=71.92768[/tex]

[tex]O\approx 72[/tex]

Therefore, the measure of angle O is 72 degrees.

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