Question

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

Assume the grid represents lengths. Count the horizontal and vertical lengths of the right - triangle formed at angle A. Let the horizontal side be 4 units and the vertical side be 3 units (based on the grid).

Step2: Use tangent function

The tangent of an angle in a right - triangle is defined as $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan(A)=\frac{3}{4}= 0.75$.

Step3: Find the angle

We know that $A=\arctan(0.75)$. Using a calculator, $A=\arctan(0.75)\approx36.87^{\circ}$.

Answer:

$36.87^{\circ}$