Given a right triangle QSR with right angle at S, if $qs$ is one leg and $qr$ is the hypotenuse, what is the measure of angle $qsr$ in degrees?

• A. $45$ degrees
• B. $90$ degrees
• C. $60$ degrees
• D. $30$ degrees

Answer: (B)

Verified step by step guidance

1. Identify the given elements in the right triangle QSR: the right angle is at vertex S, side QS is one leg adjacent to angle QSR, and side QR is the hypotenuse opposite the right angle.
2. Recall that in a right triangle, the hypotenuse is the longest side and is opposite the right angle, so angle QSR is one of the acute angles adjacent to side QS.
3. Use the definition of the cosine function for angle QSR: \(\cos(\angle QSR) = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{QS}{QR}\).
4. Calculate the measure of angle QSR by taking the inverse cosine (arccos) of the ratio \(\frac{QS}{QR}\): \(\angle QSR = \arccos\left(\frac{QS}{QR}\right)\).
5. Convert the angle from radians to degrees if necessary, to express the measure of angle QSR in degrees.