Question

Solve for x. Round to the nearest tenth, if necessary.
x=

Answer 1

Explanation:

For RIGHT triangles the cos of an angle = adjacent LEG / hypotenuse

so for THIS triangle cos 55° = x / 9.3

re-arrange to 9.3 * cos 55° = x

use calculator to find x = ~ 5.3 units (rounded)

Answer 2

x = 5.3

Explanation:

As triangle XYZ is a right triangle, and we have been given angle X, the side adjacent the angle, and the hypotenuse, we can use the cosine trigonometric ratio to solve for x.

`\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=(A)/(H)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

Given:

• θ = 55°
• A = x
• H = 9.3

Substitute the given values into the formula and solve for x:

`\implies \cos 55^(\circ)=(x)/(9.3)`

`\implies x=9.3 \cos 55^(\circ)`

`\implies x=5.3342608...`

`\implies x=5.3\; \sf (nearest\;tenth)`

Therefore, the value of x is 5.3 to the nearest tenth.