1 Answer

Miroslav Savovski · Answer 1 · 2021-07-20T06:01:39+0000

Given:

∠M = 0.775 radians, m = 5 ft, n = 7 ft, p = 4 ft

To find:

The measure of angle P.

Solution:

Using law of cosine:

$p^2=m^2+n^2-2mn \cos P$

Substitute the given values.

$4^2=5^2+7^2-2* 5 * 7 \cos P$

$16=25+49-70 \cos P$

$16=74-70 \cos P$

Subtract 74 from both sides.

$16-74=74-70 \cos P-74$

$-58=-70 \cos P$

Multiply by -70 on both sides.

$$ (-58)/(-70) =(-70 \cos P)/(-70)$

$$ (29)/(35) = \cos P$

$$\cos^(-1) (29)/(35) = P$

$$34^\circ = P$

The measure of angle P is 34°.

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