Question

Solve for x. Round to the nearest tenth of a degree, if necessary

Answer 1

x = 28.2°

Explanation:

In a right-angled triangle, we can use trigonometric ratios to relate the sides of the triangle. The tangent of an angle
`\sf x` in a right-angled triangle is given by:

`\sf \tan(x) = \frac{\textsf{Opposite}}{\textsf{Adjacent}}`

In this case,

we have the opposite side (
`\sf FG`) as 38 and the adjacent side (
`\sf GH`) as 71.

Therefore, we can write:

`\sf \tan(x) = (38)/(71)`

To find
`\sf x`, we'll take the arctangent (inverse tangent) of both sides:

`\sf x = tan^(-1)\left((38)/(71)\right)`

Now, substitute this into a calculator to get the numerical value of
`\sf x`.

`\sf x \approx tan^(-1)\left((38)/(71)\right) \approx 28.156191448272 ^\circ`

Rounding to the nearest tenth of a degree:

`\sf x \approx tan^(-1)\left((38)/(71)\right) \approx 28.2 ^\circ`

So,
`\sf x` is approximately
`\sf 28.2^\circ`.