From a point along a straight road, the angle of elevation to the top of a hill is . From farther down the road, the angle of elevation to the top of the hill is . How high is the hill?

Complete Question:

From a point along a straight road, the angle of elevation to the top of a hill is 33° . A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. How high is the hill?

The hill is 165.87 ft high

Step-by-step explanation:

Check the file attached below for a pictorial understanding of the question

From ΔABC

..........(1)

From ΔABD

............(2)

Equating (1) and (2)

Substitute the value of x into equation (1)

y = 165.87 ft

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft