Mathematics: What does x equal? Plz help, I will mark brainliest asap!!

What does x equal? Plz help, I will mark brainliest

fymdes2001

18.01.2022

X = 83°

Solution:

XY (x) = 17 ft

XZ (y) = 8 ft

ZY (z) = 16 ft

To find the angle X:

Using Law of cosine formula: $a^{2}=b^{2}+c^{2}-2 bc \cos A$

$x^{2}=y^{2}+z^{2}-2 bc \cos X$

Substitute the given values in the formula.

$17^{2}=8^{2}+16^{2}-2 (8)(16) \cos X$

$289=64+256-256 \cos X$

$289=320-256 \cos X$

Subtract 320 on both sides of the equation, we get

$-31=-256 \cos X$

Divide by –256 on both sides.

$$\frac{-31}{-256}= \cos X$

$$\cos ^{-1}\left(\frac{-31}{-256}\right)= X$

X = 83°

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