Chapter 11.1, Problem 32PPS

To determine

To calculate: The area of the given triangle.

Answer to Problem 32PPS

The area of the given triangle is $A=17.9i{n}^2$ .

Explanation of Solution

Given information: The triangle is given below.

  

Formula used:

The area of a triangle is given by

  $\begin{array}{l}A=\frac{1}{2}\times \left(b\times h\right)\\ b\text{is}\text{the}\text{base}\text{of}\text{the}\text{triangle}\text{.}\\ h\text{is}\text{the}\text{height}\text{.}\end{array}$

Calculation:

From the given information it can be observed that

  $\begin{array}{c}h=4in\&b=b_1+b_2\\ \text{Where,}\tan {31}^{\circ }=\frac{h}{b_1}\\ b_1=\frac{4}{\left(\tan {31}^{\circ }\right)}\\ b_1=\frac{4}{\left(0.60\right)}=6.66in\\ \\ \text{Where,}\tan {60}^{\circ }=\frac{h}{b_2}\\ b_2=\frac{4}{\left(\tan {60}^{\circ }\right)}\\ b_2=\frac{4}{\left(1.73\right)}=2.31in\end{array}$

So $b=b_1+b_2=6.66+2.31=8.97in$

The area of the given triangle is

  $\begin{array}{c}A=\frac{1}{2}\times \left(b\times h\right)\\ =\frac{1}{2}\times \left(8.97\times 4\right)\\ A=17.94i{n}^2\\ A=17.9i{n}^2\end{array}$

Therefore the area of the given triangle is $A=17.9i{n}^2$ .