Question

Find the sine of each acute angle in the triangle below. Select all that apply.

Answer 1

Given

To find the sine of each acute angle.

Now,

The sine of an angle in a right triangle is given by,

$\sin \theta=\frac{opposite\text{ side}}{hypotnuse}$

In a right triangle ABC, angle A and angle C are the acute angles, since angle B is 90 degrees (right angle).

Then,

$\begin{gathered} \sin A=\frac{BC}{AC} \\ =\frac{9}{41} \\ \sin C=\frac{AB}{AC} \\ =\frac{40}{41} \end{gathered}$

Hence, the sine of each acute angles in the triangle is 9/41 and 40/41.