Application (Right Triangle Trigonometry)

Michigan State University - Diagnostic Exam

Suppose that the angle of elevation from a point on level ground to the top of a pole is 40^∘. From another point, 8 meters further away, the angle of elevation is 30^∘. Let x be the distance from the base of the pole to the nearest point. Then x satisfies which of the following?

a) 10 < x < 12 b) 12 < x < 14 c) 14 < x < 16

d) 16 < x < 18 e) 18 < x < 20

Solution:

Let h be the height of the pole. Then the statements imply

∘ tan40 = h∕x tan30 ∘ = h∕ (8 + x )

Thus

∘ ∘ xtan 40 = (8 + x )tan30

so that

∘ x = ----8tan-30------ tan 40∘ - tan 30∘ ≈ 17.6459

Diagnostic:

July 15, 2008