Chapter 9.7, Problem 24E

To determine

Tofind:Ares of the given triangle

Answer to Problem 24E

  $A=137.37$

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-

  $\begin{array}{l}\tan \angle Z=\frac{opposite}{adjacent}\\ \Rightarrow \tan {70}^{\circ }=\frac{a}{10}\\ \Rightarrow 2.7474=\frac{a}{10}\\ \Rightarrow a=\left( 2.7474\right)10\\ \Rightarrow a= 27.474\end{array}$

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

  $\begin{array}{l}\Rightarrow A=\frac{1}{2}\left(10\right)\left(27.474\right)\\ \Rightarrow A=\frac{1}{2}\left(274.74\right)\\ \Rightarrow A=137.37\end{array}$