Chapter 9.7, Problem 25E

To determine

Tofind:Ares of the given triangle

Answer to Problem 25E

  $A=79.9196$

Explanation of Solution

Given information:

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 definition we can say-

  $\begin{array}{l}\tan \angle F=\frac{opposite}{adjacent}\\ \Rightarrow \tan {36}^{\circ }=\frac{a}{22}\\ \Rightarrow 0.7265=\frac{a}{10}\\ \Rightarrow a=\left( 0.7265\right)10\\ \Rightarrow a= 7.265\end{array}$

Area of triangle $A=\frac{1}{2}bh$

  $\begin{array}{l}\Rightarrow A=\frac{1}{2}\left(22\right)\left( 7.265\right)\\ \Rightarrow A=\frac{1}{2}\left(274.74\right)\\ \Rightarrow A=\frac{159.8393}{2}\\ \Rightarrow A=79.9196\end{array}$