Question

jessica is standing 20 feet away from a skyscraper in new york when she measures the angle to the top of the building as 88.8 . how tall is the building ?

Answer 1

let h be the height of the building

tan 88.8 = h / 20
h = 20 * tan 88.8 = 954.79 feet

Answer 2

The building is 954.8 feet tall .

Explanation:

Now by using the trignometric identity

`tan \theta = (Perpendicular)/(Base)`

As given

jessica is standing 20 feet away from a skyscraper in new york when she measures the angle to the top of the building as 88.8 ° .

`\theta = 88.8^(\circ)`

Perpendicular = AB

Base = BC = 20 feet

Put all the values in the trignometric identity .

`tan\ 88.8^(\circ)= (AB)/(BC)`

`tan\ 88.8^(\circ)= (AB)/(20)`

tan 88.8 ° = 47.74 (Approx)

AB = 20 × 47.74

AB = 954.8 feet

Therefore the building is 954.8 feet tall .