Chapter 11.3, Problem 53STP

To determine

To find: Length of side of rectangle ABCD.

Answer to Problem 53STP

Length of Side AB = 41.6 feet.

Explanation of Solution

Given Information:

ABCD is a Rectangle, length of Diagonals = 56 ft.

  $m\angle BAC=42°$

Figure:

  

The Diagonals of the Rectangle are congruent, thus Length of the diagonal AC = 56 ft, where $\angle B=90°$ .

Using the Cosine Rule for Right angle Triangle,

  $\text{Cosθ = }\frac{\text{Base}}{\text{Hypotenuse}}$

In this case,

  $\text{CosA=}\frac{\text{AB}}{\text{AC}}$

Where,

AB = Base / Adjacent Side of $\angle A$

AC = Hypotenuse (Side opposite to Right Angle)

  $\begin{array}{l}\Rightarrow \text{Cos42° = }\frac{\text{AB}}{\text{56}}\\ \Rightarrow \text{AB = Cos42°×56}\\ \Rightarrow \text{AB = 0}\text{.743×56}\\ \Rightarrow \text{AB = 41}\text{.60 ft}\text{.}\end{array}$

Thus,

Length of Side AB = 41.6 feet.