Chapter 8.4, Problem 53PPS

To determine

The perimeter and area of the triangle.

Answer to Problem 53PPS

  $\begin{array}{l}P=8.73\text{ft}\\ A=3.41{\text{ft}}^2\end{array}$

Explanation of Solution

Given:

The given angle is:

Calculation:

Let y be the length of the altitude to the base.

According to the definition of the Cosine function,

  $\begin{array}{l}\cos 48°=\frac{1.75}{x}\\ x=\frac{1.75}{\cos 48°}\\ x=2.615\end{array}$

According to the definition of the Tangent function,

  $\begin{array}{l}\tan 48°=\frac{y}{1.5}\\ 12\tan 48°=y\\ y=1.95\end{array}$

The perimeter of the triangle will be:

  $\begin{array}{l}P=3.5+2.615+2.615\\ P=8.73\text{ft}\end{array}$

The area of the triangle will be:

  $\begin{array}{l}A=\frac{1}{2}bh\\ A=\frac{1}{2}\left(3.5\right)\left(1.95\right)\\ A=3.41{\text{ft}}^2\end{array}$