Question

You hike 190 meters up a steep hill that has a 33∘ angle of elevation as shown in the diagram.

Answer 1

a = 103 m

b = 159 m

angle B is 57

Explanation:

Answer 2

b = 159 m

a = 103 m

angle B is 57 degrees

Explanation:

Let’s start with getting the measure of angle B

Mathematically, since we have a right triangle , we have to subtract the given angle from 90 to get the other acute angle

So we have the measure of B as;

90-33 = 57 degrees

To get the value of a, we use the appropriate trigonometric ratio

a faces the angle 33, that makes it an opposite to that angle

190 faces the right angle and that makes it the hypotenuse

Mathematically , the relationship between the two is that trigonometrically, they are related by the sine which is the ratio of the opposite to the hypotenuse

so, we have it that;

sine 33 = a/190

a = 190 * sine 33

a = 103 m

to get b, it is adjacent to the given angle

So with the hypotenuse, the ratio between it and the hypotenuse is the cosine

so;

cos 33 = b/190

b = 190 * cos 33

b = 159 m