Question

in triangle rst, rs = 9 and m∠r = 40°, find the length of \\(\overline{st}\\) to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute given values

$\sin(40^\circ)=\frac{ST}{9}$

Step3: Solve for $ST$

$ST = 9\times\sin(40^\circ)$

Step4: Calculate the value

$ST\approx9\times0.6428\approx5.8$

Answer:

5.8