Chapter 9, Problem 10CST

To determine

Tofind:The value of $r$

Answer to Problem 10CST

  $r\approx 4$

Explanation of Solution

Given information:

Concept Used:

In a right-angled triangle ABC, sine for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of hypotenuse and cosine of acute angle $\angle A$ is the ratio of length of side adjacent to angle $\angle A$ to the length of hypotenuse.

Calculation:

Basis definition we can say-

  $\begin{array}{l}\sin R=\frac{Opposite}{Hypotenuse}\\ \Rightarrow \sin {21}^{\circ }=\frac{PQ}{PR}\\ \Rightarrow 0.3583=\frac{r}{10}\\ \Rightarrow r=10\left(0.35836\right)\\ \Rightarrow r=3.5836\\ \Rightarrow r\approx 4\end{array}$