Question

applying the 30°-60°-90° and 45°-45°-90° relationships isaiah sketches a model of a skateboard ramp. the model has two surfaces on which to skate, represented by sides ab and ad in the diagram. the steepest side of the model, ab, measures 4 inches. what is the length of the other skating surface, ad? 2√2 in. 2√3 in. 4√2 in. 4√3 in.

Explanation:

Step1: Find height AC (45-45-90 triangle)

In $\triangle ABC$, it is a 45°-45°-90° triangle, so leg $AC = AB \cdot \sin(45^\circ)$.
$AC = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2}$

Step2: Find AD (30-60-90 triangle)

In $\triangle ACD$, $\angle D=30^\circ$, so hypotenuse $AD = \frac{AC}{\sin(30^\circ)}$.
$AD = \frac{2\sqrt{2}}{\frac{1}{2}} = 4\sqrt{2}$

Answer:

$4\sqrt{2}$ in.