Question

michelle is building a dog pen as shown in the scale drawing below. the line segments represent a fence enclosing the pen, with an opening to allow the dogs to enter and exit. each small square in the scale drawing represents a square with a side length of 3 feet. each marked point is at the vertex of a small square in the drawing. what is the measure of the angle labeled a in the scale drawing of the dog pen?

Explanation:

Step1: Identify right - triangle sides

Count the grid - squares. The vertical side of the right - triangle containing angle $A$ has 4 small squares and the horizontal side has 3 small squares. Since each small square side length is 3 feet, the vertical side length $y = 4\times3=12$ feet and the horizontal side length $x = 3\times3 = 9$ feet.

Step2: Use tangent function

The tangent of an angle in a right - triangle is defined as $\tan(A)=\frac{y}{x}$. Substituting $y = 12$ and $x = 9$, we get $\tan(A)=\frac{12}{9}=\frac{4}{3}$.

Step3: Find the angle

We know that if $\tan(A)=\frac{4}{3}$, then $A=\arctan(\frac{4}{3})$. Using a calculator, $A\approx53.13^{\circ}$.

Answer:

$53.13^{\circ}$