In triangle PQR, PR = 7.6 cm and angle PRQ = 30 degrees. PS is an altitude. Find PS.

Question

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Identify the given information from the diagram.
We have a triangle PQR.
The length of side $PR = 7.6$ cm.
The angle $\angle PRQ = 30^\circ$ is labeled in the diagram.
Point S is on the side QR, and PS is shown as an altitude, meaning $\angle PSR = 90^\circ$ .
Calculate $\angle PRQ$ .
The value for $\angle PRQ$ is directly given in the diagram.
$\angle PRQ = \boxed{30^\circ}$
Calculate PS.
Consider the right-angled triangle $\triangle PRS$ . We know the hypotenuse $PR = 7.6$ cm and the angle $\angle PRQ = 30^\circ$ . We want to find the side PS, which is opposite to $\angle PRQ$ .
We use the sine function:
$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$ $\sin(\angle PRQ) = \frac{PS}{PR}$
Substitute the known values and solve for PS.
$\sin(30^\circ) = \frac{PS}{7.6 \text{ cm}}$
We know that $\sin(30^\circ) = 0.5$ .
$0.5 = \frac{PS}{7.6 \text{ cm}}$ $PS = 7.6 \text{ cm} \times 0.5$ $PS = \boxed{3.8 \text{ cm}}$

Answer