Question

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: Analyze right - triangle ABC

In right - triangle ABC with $\angle B = 45^{\circ}$ and $AB = 4$ inches. Since $\angle B=45^{\circ}$, it's a 45 - 45 - 90 triangle. So $AC = BC=\frac{AB}{\sqrt{2}}=\frac{4}{\sqrt{2}} = 2\sqrt{2}$ inches.

Step2: Analyze right - triangle ACD

In right - triangle ACD, $\angle D = 30^{\circ}$, and $AC = 2\sqrt{2}$ inches. We know that $\sin D=\frac{AC}{AD}$. So $AD=\frac{AC}{\sin30^{\circ}}=\frac{2\sqrt{2}}{\frac{1}{2}} = 4\sqrt{2}$ inches.

Answer:

$4\sqrt{2}$ in.