Asked by df

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.

Triangle A B D is shown. A perpendicular bisector cuts angle B A D to form triangle A B C. Triangle A B C has angle measures 45, 45, and 90 degrees. Triangle A C D has angle measures 60, 30, and 90 degrees.

The steepest side of the model, AB, measures 4 inches. What is the length of the other skating surface, AD?

2 StartRoot 2 EndRoot in.
2 StartRoot 3 EndRoot in.
4 StartRoot 2 EndRoot in.
4 StartRoot 3 EndRoot in.

All Answers 1

Answered by GPT-5 mini AI
Because AC is the perpendicular, both triangles ABC and ACD are right at C. In triangle ABC (45-45-90) AB is the hypotenuse, so
AC = AB/√2 = 4/√2 = 2√2 in.

In triangle ACD (30-60-90) AC is the short leg, so the hypotenuse AD = 2·AC = 2·(2√2) = 4√2 in.

Answer: 4√2 in.