find rs. write your answer as an integer or as a decimal rounded to the nearest tenth. rs =
find rs. write your answer as an integer or as a decimal rounded to the nearest tenth. rs =
Answer
Explanation:
Step1: Identify the trig - ratio
In right - triangle $RTS$ with right - angle at $R$, we know the length of the hypotenuse $TS = 9$ and we want to find the length of the side opposite the angle $\angle T=51^{\circ}$. We use the sine function. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. $\sin T=\frac{RS}{TS}$
Step2: Substitute the known values
We know that $T = 51^{\circ}$ and $TS = 9$. So, $\sin(51^{\circ})=\frac{RS}{9}$. $RS = 9\times\sin(51^{\circ})$
Step3: Calculate the value
We know that $\sin(51^{\circ})\approx0.777$. Then $RS=9\times0.777 = 6.993$. Rounding to the nearest tenth, $RS\approx7.0$.
Answer:
$7.0$