Question

What are the centimeters to the nearest tenth of the hypotenuse and leg?

Answer 1

Answer:

Hypotenuse = 10.4cm

Leg = 6.7cm

Explanation:

Let x represent the unknown leg of the triangle.

To be able to find x, we have to take the tangent of angle 40 degrees as shown below;

$\begin{gathered} \tan 40=\frac{x}{8} \\ 8\tan 40=x \\ x=6.7\operatorname{cm} \end{gathered}$

Let y represent the length of the hypotenuse.

To find y, we have to take the cosine of angle 40 degrees;

$\begin{gathered} \cos 40=\frac{8}{y} \\ y\cos 40=8 \\ y=\frac{8}{\cos 40} \\ y=10.4\operatorname{cm} \end{gathered}$