Question

which expression gives the area of triangle qrs? triangle image with sides labeled 15, 11, 9 and angle 20° at r options: a. $\frac{1}{2}(11)(15)sin(20^circ)$ b. $\frac{1}{2}(11)(15)cos(20^circ)$ c. $\frac{1}{2}(9)(15)sin(20^circ)$ d. $\frac{1}{2}(9)(15)cos(20^circ)$

Explanation:

Step1: Recall area formula for SAS triangle

The area of a triangle with two sides $a, b$ and included angle $\theta$ is $\frac{1}{2}ab\sin\theta$.

Step2: Identify sides and included angle

In $\triangle QRS$, sides adjacent to the $20^\circ$ angle are $RQ=9$ and $RS=15$.

Step3: Substitute values into formula

Area = $\frac{1}{2} \times 9 \times 15 \times \sin(20^\circ)$. This matches option C.

Answer:

C. $\frac{1}{2}(9)(15)\sin(20^\circ)$