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vagabundo [1.1K]
2 years ago
11

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.

Mathematics
2 answers:
AysviL [449]2 years ago
3 0

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

taurus [48]2 years ago
3 0

Answer:

14°

Step-by-step 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.

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

<em />

Sin\theta=\frac{opposite}{hypotenuse}=\frac{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°

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