Question

A bike ramp is shown in the figure. What is theta, the bike ramp's angle of elevation? Round your answer to the nearest degree. Enter your answer in the box.

Answer 1

14°

Explanation:

Looking at the triangle with green border,

with respect to the angle
`\theta`, the side 1.5 ft is "opposite" and the side 6 ft is "hypotenuse" of the triangle.

Which trigonometric ratio relates opposite with hypotenuse? It is sine. Thus we can write:

`Sin\theta=(opposite)/(hypotenuse)=(1.5)/(6)=0.25\\Sin\theta=0.25\\\theta=Sin^(-1)(0.25)=14.48`

Hence, the angle is 14.48°

rounded to nearest degree, it is 14°

Answer 2

Ф = 14° ⇒ to the nearest degree

Explanation:

* Lets revise the trigonometry functions

- Assume that we have a right triangle ABC

∵ m∠B = 90°

∴ AC is the hypotenuse ⇒ opposite to the right angle

∴ AB and BC are the legs of the right angles

- Let angle ACB called Ф

∵ sinФ = opposite/hypotenuse

∴ sinФ = AB/AC

∵ cosФ = adjacent/hypotenuse

∴ cosФ = BC/AC

∵ tanФ = opposite/adjacent

∴ tanФ = AB/BC

* Now lets solve the problem

- We will consider the bike ramp is the ΔABC

∵ AB = 1.5 feet

∵ ∠ACB is Ф

∵ The length of the ramp is the hypotenuse

∴ AC = 6 feet

- W have the length of the opposite to Ф and the hypotenuse

∴ We will chose the sin function

∵ sinФ = AB/AC

∴ sinФ = 1.5/6 ⇒ use the inverse of sin to find Ф

∴ Ф = sin^-1 (1.5/6) = 14.47 ≅ 14° ⇒ to the nearest degree