Answer:
Ф = 14° ⇒ to the nearest degree
Step-by-step 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
students.