Question

A ramp 20 ft. in length rises to a platform that is 18 ft. off the ground. How do you find x, the angle of elevation of the ramp?

Answer 1

Hint: We will first draw its figure to have an idea about the angle. Then, we will observe that the perpendicular is 18 ft. and the hypotenuse is 20 ft. Thus, we get the angle using sine ratio.

Complete step by step solution:
We are given that we are required to find x, the angle of elevation of the ramp when a ramp which is 20 ft. high in length rises to a platform which is 18 ft. off the ground.
Let us draw its diagram to get a better view of the same situation.

Here, in the above picture, AC is the ramp which is 20 ft. long and it is put 18 ft. off the ground which is visible with AB.
Now, we can clearly see that according to angle C, we have AB as the perpendicular and AC is the hypotenuse of the triangle ABC.
Since, we know that the ratio of perpendicular and the hypotenuse is given by the sine of the angle, thus we have:-
$ \Rightarrow \sin \theta = \dfrac{P}{H}$
Putting AB instead of P and AC instead of H, we will then obtain the following equation with us:-
$ \Rightarrow \sin \theta = \dfrac{{AB}}{{AC}}$
Putting the values as given, we will then obtain the following equation with us:-
$ \Rightarrow \sin \theta = \dfrac{{18}}{{20}}$
Crossing – off 2 from both the numerator and denominator, we will then obtain the following equation with us:-
$ \Rightarrow \sin \theta = \dfrac{9}{{10}}$
We can write this as follows:-
$ \Rightarrow \theta = {\sin ^{ - 1}}\left( {\dfrac{9}{{10}}} \right)$
Thus, we have the required answer.

Note:
The students must note that the difference between perpendicular and base is with respect to the angle whose sine, cosine or tangent we are looking for. The side which is incident with the angle other than hypotenuse is the base and the other left side is known as the perpendicular.
The students must also note that this is only applicable in a right angled triangle.
The students must also note that we could cross 2 off from both the numerator and denominator because we are sure that 2 can never be equal to 0.