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=(BC)/(AC) \\ =(9)/(41) \\ \sin C=(AB)/(AC) \\ =(40)/(41) \end{gathered}`

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