Question

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

Explanation:

Step1: Recall area - of - triangle formula

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

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

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

Step3: Substitute 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:

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