Question

A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the ramp and the freeway?

Answer 1

The ramp,the rise and the base, when illustrated, will form a right triangle. The hypotenuse is the ramp which measures 200 ft long. The rise is the vertical height which measures 37 feet. As you can see in the picture, the arc drawn below the ramp to the horizontal line directing to the freeways is the unknown angle that we have to find.

First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:

cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°

Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,

β = 90° + 79.34°
β = 169.34°  

Answer 2

A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is

$\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}$

From the information given:

The  measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:

$\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}$

$\mathbf{sin \theta = \dfrac{37}{200}}$

$\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}$

$\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}$

Therefore, the measure of the angle formed between the ramp and the freeway is

$\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}$

Learn more about the sine rule here:

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