Question

20 POINTS! WRONG ANSWERS WILL BE REPORTED!

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?

A) 2 square root 2
B) 2 square root 3
C) 4 square root 2
D) 4 square root 3

Answer 1

(C)

Explanation:

It is given that The steepest side of the model, AB, measures 4 inches, thus

From ΔABC, using the trigonometry, we have

`(AC)/(AB)=sin45^(\circ)`

Substituting the given value, we have

⇒
`(AC)/(4)=sin45^(\circ)`

⇒
`AC=4{*}(1)/(√(2))`

⇒
`AC=2√(2)`

Now, from ΔACD, we have

`(AC)/(AD)=sin30^(\circ)`

⇒
`(2√(2))/(AD)=(1)/(2)`

⇒
`AD=4√(2)`

Therefore, the length of AD will be
`4√(2)`

thus, option C is correct.

Answer 2

triangle ABC 45-45-90
AB = 4 so AC = 2 square root 2

triangle ACD 30-60-97
AC = 2 square root 2
AD = 2(AC)
AD = 4 square root 2

answer is

C) 4 square root 2