Question

A right triangle has side length 8,15, and 17 as shown below.

Answer 1

In any right triangle, you have the following properties: if you want to know the cosine of an angle, it is given by the ratio between the adjacent leg and the hypothenuse.

Similarly, the sine of an angle it is given by the ratio between the opposite leg and the hypothenuse.

So, if you focus on the angle X, the adjacent leg is 15 units long, and the opposite leg is 8 units long. The hypothenuse is 17 units long.

So, we have

$\cos(x) = \dfrac{\text{adjacent}}{\text{hypothenuse}} = \dfrac{15}{17}$

$\sin(x) = \dfrac{\text{opposite}}{\text{hypothenuse}} = \dfrac{8}{17}$

To compute the tangent, simply use its definition:

$\tan(x) = \dfrac{\sin(x)}{\cos(x)} = \dfrac{\frac{8}{17}}{\frac{15}{17}} = \dfrac{8}{15}$