Question
A ramp on a moving truck makes a 30° angle with the ground. The length of the ramp if it is? 5 ft tall? Round to the 10ths place (one decimal place) if necessary.
- 10
- 20
- 30
- 40
Hint:
We are given that the ramp makes 30° angle with the moving truck. We are given its height. It is 5ft tall. The height of the ramp makes 90° angle with the ground. We are asked to find the length of the ramp. It means the length of hypotenuse.
The correct answer is: 10
Let the ramp be denoted by ∆ABC.
∠ABC = 90°
∠BCA = 30°
AB = 5
We have to find the length of side AC.
The sum of all angles of a triangle is 180°. Therefore, the remaining angle will be 60°
So, ∠BAC = 60°
It is 30°-60°-90° triangle.
In a 30°-60°-90° triangle, the length of hypotenuse is two times the length of the smallest side. It’s longer side is √3 times the value of the smallest side.
The side opposite to the 30° angle is the smallest side.
The side opposite to the 60° angle is the longer side.
In the given question, the side opposite to 30° is AB.
Length of hypotenuse = 2(length of smaller side)
AC = 2(AB)
= 2(5)
AC = 10
The length of the ramp is 10.
For such questions, we should know about the properties of a right-angled triangle and 30°-60°-90° triangle. The alternate way to solve the above question is by Pythagoras theorem and trigonometric ratios.
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