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.

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.

Answer 1

The length of the other skating surface AD of the ramp is 4√2 inches

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Sine rule shows the relationship between the sides and angles of a triangle.

Using sine rule:

AB / sinD = AD / sinB

4/sin(30) = AD / sin(45)

AD = 4√2 inches

The length of the other skating surface AD of the ramp is 4√2 inches

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