Question

Find the blank in degrees round to the nearest tenth

Answer 1

If θ is one of the acute angles in a right triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side.

From this, we get the following equation for alpha

`\sin \alpha=\frac{3}{\sqrt[]{58}}`

Calculating the arcsine on both sides of the equation, we have

`\begin{gathered} \arcsin \sin \alpha=\arcsin \frac{3}{\sqrt[]{58}} \\ \alpha=\arcsin \frac{3}{\sqrt[]{58}} \\ \alpha=23.1985905136\ldots \\ \alpha\approx23.2 \end{gathered}`