Question

question in △rst, r = 5.9 inches, s = 3 inches and ∠t = 57°. find the area of △rst, to the nearest 10th of a square inch. answer attempt 1 out of 2 in² submit answer watch video show examples

Explanation:

Step1: Recall area formula for triangle

The area formula for a triangle with two - side lengths \(r\) and \(s\) and included - angle \(\angle T\) is \(A=\frac{1}{2}rs\sin T\).

Step2: Substitute given values

We are given \(r = 5.9\) inches, \(s = 3\) inches, and \(\angle T=57^{\circ}\). First, find the sine of \(57^{\circ}\). Using a calculator, \(\sin(57^{\circ})\approx0.8387\). Then substitute \(r = 5.9\), \(s = 3\), and \(\sin T\approx0.8387\) into the formula \(A=\frac{1}{2}rs\sin T\). So \(A=\frac{1}{2}\times5.9\times3\times0.8387\).

Step3: Calculate the area

\(A=\frac{1}{2}\times5.9\times3\times0.8387=\frac{1}{2}\times17.7\times0.8387 = 8.85\times0.8387\approx7.4\) square inches.

Answer:

\(7.4\) square inches