Question

Right Triangle Trigonometry: A streetlight stands perpendicular to the ground. Martin measured the shadow of the streetlight. The distance between the base of the streetlight and the tip of the shadow is 15 feet. In terms of this situation, what could the expression below represent?

tan^−1( 10/15)

a) The distance between the tip of the shadow and the top of the streetlight if the angle of elevation from the tip of the shadow to the top of the streetlight is 10 degrees
b) The angle of elevation from the tip of the shadow to the top of the streetlight if the streetlight is 10 feet tall
c) The angle of elevation from the tip of the shadow to the top of the streetlight if the distance between the tip of the shadow and the top of the streetlight is 10 feet
d) The height of the streetlight if the angle of elevation from the tip of the shadow to the top of the streetlight is 10 degrees

Answer 1

The expression tan−¹(10/15) calculates the angle of elevation from the tip of the shadow to the top of a 10 feet tall streetlight.

Step-by-step explanation:

The expression tan−¹(10/15) represents the angle of elevation from the tip of the shadow to the top of the streetlight if the streetlight is 10 feet tall. This can be understood as follows: in a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. Here, the streetlight is the opposite side (10 feet), and the shadow is the adjacent side (15 feet). The inverse tangent or arctangent function, written as tan−¹, lets us find the angle when we know the opposite and adjacent sides. Therefore, tan−¹(10/15) gives us the angle of elevation from the shadow tip to the streetlight top.