Question

select the correct answer. which expression gives the area of triangle qrs? a. $\frac{1}{2}(9)(15)\cos(20^{\circ})$ b. $\frac{1}{2}(11)(15)\sin(20^{\circ})$ c. $\frac{1}{2}(9)(15)\sin(20^{\circ})$ d. $\frac{1}{2}(11)(15)\cos(20^{\circ})$

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle when two - side lengths \(a\) and \(b\) and the included angle \(\theta\) is given is \(A=\frac{1}{2}ab\sin\theta\).

Step2: Identify the values of \(a\), \(b\), and \(\theta\) in \(\triangle QRS\)

In \(\triangle QRS\), let \(a = 9\), \(b=15\), and \(\theta = 20^{\circ}\) (the included angle between the sides of lengths \(9\) and \(15\)).

Step3: Substitute the values into the formula

Substituting \(a = 9\), \(b = 15\), and \(\theta=20^{\circ}\) into the formula \(A=\frac{1}{2}ab\sin\theta\), we get \(A=\frac{1}{2}(9)(15)\sin(20^{\circ})\).

Answer:

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