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Chapter 10: Q67. (page 660)

How long is the ramp?

Short Answer

Expert verified

The ramp is6feet long.

Step by step solution

01

Step 1. Given. 

The triangle is given with the following dimension

02

Step 2. Write the formulas for the trigonometric ratios.

The formula for the trigonometric ratios is:

sin∠A=legopposite∠Ahypotenusecos∠A=legadjacentto∠Ahypotenusetan∠A=legopposite∠Alegadjacentto∠A

03

Step 3. Determine the length of the ramp.

The given diagram is:

Since in the diagram, the side opposite to the angle having measure30° is given and it is required to a find the hypotenuse which is the length of the ramp. Therefore, use the sine ratio.

From the diagram, it can be noticed that the leg opposite30° and hypotenuse are 3, and x respectively.

Therefore,

sin30°=legopposite30°hypotenuse12=3x1×x=2×3x=6

Therefore, the ramp is 6 feet long.

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