Chapter 9, Problem 32CR

To determine

Tofind:The length of side opposite to $\angle P$

Answer to Problem 32CR

  $25$

Explanation of Solution

Given information:

Right triangle $\Delta PQR$

  $\angle P={72}^{\circ }$

Length of side adjacent to $\angle P$ is 8 units

Concept Used:

In a right-angled triangle ABC, tangent for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of side adjacent to $\angle A$

Calculation:

Basis the given information, the triangle would be-

Basis definition we can say-

  $\begin{array}{l}\tan P=\frac{opposite}{adjacent}\\ \Rightarrow \tan {72}^{\circ }=\frac{RQ}{PR}\\ \Rightarrow 3.0776=\frac{x}{8}\\ \Rightarrow x=8\left(3.0776\right)\\ \Rightarrow x=24.6214\\ \Rightarrow x\approx 25\end{array}$