Question

Use what you know about sine, cosine, and tangent to calculate the height of the buildings in the diagram below.

Answer 1

x = 32 feet

Explanation:

By applying tangent rule in ΔACD,

tan(40°) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

=
`(AB+AC)/(CD)`

=
`(x+BC)/(87)`

x + BC = 73 -----(1)

By applying tangent rule in ΔBCD,

tan(25°) =
`(BC)/(CD)`

=
`(BC)/(87)`

BC = 40.57

By substituting the value of BC in equation (1),

x + 40.57 = 73

x = 32.43

x ≈ 32 feet