Question

HELP! Showing all work, solve for x and y and round to nearest tenth

Answer 1

x = 67.4°

y = 22.6°

Explanation:

The tangent ratio is a trigonometric ratio that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle.

`\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}`

Angle x

The side opposite angle x is 7.2, and the side adjacent angle x is 3.

Use the tangent trigonometric ratio to find the measure of angle x:

`\begin{aligned}\tan(x)&=(7.2)/(3)\\x&=\tan^(-1)\left((7.2)/(3)\right)\\x&=\vphantom{\frac12}67.380135...^(\circ)\\x&=67.4^(\circ)\;\sf (nearest\;tenth)\end{aligned}`

Therefore, x = 67.4°.

Angle y

The side opposite angle y is 3, and the side adjacent angle y is 7.2.

Use the tangent trigonometric ratio to find the measure of angle y:

`\begin{aligned}\tan(y)&=(3)/(7.2)\\y&=\tan^(-1)\left((3)/(7.2)\right)\\y&=\vphantom{\frac12}22.6198649...^(\circ)\\y&=22.6^(\circ)\;\sf (nearest\;tenth)\end{aligned}`

Therefore, y = 22.6°.