Question

In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches. Find the measure of ∠P to the nearest degree.

Answer 1

Given:

In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches.

To find:

The measure of ∠P to the nearest degree.

Solution:

According to the law of cosine:

$\cos A=\dfrac{b^2+c^2-a^2}{2bc}$

Using law of cosine in triangle NOP, we get

$\cos P=\dfrac{n^2+o^2-p^2}{2no}$

Putting the given values, we get

$\cos P=\dfrac{(910)^2+(110)^2-(820)^2}{2(910)(110)}$

$\cos P=\dfrac{828100+12100-672400}{200200}$

$\cos P=\dfrac{167800}{200200}$

$\cos P=0.83816$

Taking cos inverse on both sides, we get

$P=\cos^{-1}(0.83816)$

$P=(33.05367)^\circ$

$P\approx 33^\circ$

Therefore, the measure of ∠P is 33°.

Answer 2

33° is the answer.

kinda in a hurry, but this is the answer to Deltamath