Question

Find x. Round your answer to the nearest tenth of a degree.

Answer 1

Answer: $x=49.6^{\circ}$

Step-by-step explanation:

In the given figure , we have right triangle with hypotenuse 21 units and the side opposite to angle x is 16 units.

According to the trigonometry,

$\sin \theta = \dfrac{\text{side opposite of }\theta}{\text{Hypotenuse}}$

So for , the given figure , we have

$\sin x = \dfrac{16}{21}\\\\\Rightarrow\ \sin x\approx0.7619\\\\\Rightarrow\ x=\sin^{-1}(0.7619)=0.8662\text{ radian}$ (using sine calculation)

Convert radian into degrees , we have

$x=0.8662\times\dfrac{180^{\circ}}{\pi}\\\\=0.8662\times\dfrac{180^{\circ}}{3.14159}=49.6319852107\approx49.6^{\circ}$  [Round to the nearest tenth.]

Hence, $x=49.6^{\circ}$

Answer 2

In the given right triangle, x = 49.6°

Missing angles of right triangles

The triangle shown is a right triangle

The angle, θ = x

The opposite = 16

The hypotenuse = 21

Using the formula:

$sin \theta = \frac{opposite}{hypotenuse}$

Substitute opposite = 16, hypotenuse = 21, and θ = x into the formula above to solve for x

$sin x = \frac{16}{21} \\\\sin x = 0.7619\\\\x = sin^{-1}0.7619\\\\x=49.6^0$

Therefore, in the given right triangle, x = 49.6°

Learn more on missing angles of right triangles here: https://brainly.com/question/12318575