Question

Should be pretty easy to answer, I just need a refresher. I forgot how to solve for triangles...

Answer 1

x = 25.734083

`x \approx 25.734`

Explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

Note we are given an angle of 25°. The opposite side is 12 and the adjacent side is x. We need to relate those sides with a trig function (the tangent ratio)

Tangent Ratio:

`\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}`

Substituting:

`\displaystyle \tan 25^\circ=(12)/(x)`

Solving for x:

`\displaystyle x=(12)/(\tan 25^\circ)`

Calculating:

`\displaystyle x=(12)/(0.466307)`

x = 25.734083

Round to 3 decimals:

`\mathbf{x \approx 25.734}`