Question

Given sin(theta)=3/5, find a, the other angle in the right triangle.

Answer 1

In the given triangle, one angle is a right angle.

Given $\sin \Theta =\frac{3}{5}$

$\Theta =\arcsin \frac{3}{5}$

$\Theta = 36.8^{\circ}=37^{\circ}$

So, the other angle is 37 degrees.

Now, we have to find the third angle.

By using angle sum property in a triangle.

$90^{\circ}+37^{\circ}+$+ third angle = $180^{\circ}$

Third angle = $180^{\circ}-127^{\circ}$

= $53^{\circ}$

So, the other angles are 37 degrees and 53 degrees.

Answer 2

$\sin( \alpha ) = \frac{3}{5} \\ \alpha = 37 \\ \beta = 53$