Question

John stands on the first floor of his apartment that is 80 m from the multistoreybuilding. As a mathematician, he measures the angle of elevation to the top of themultistorey building as 22º and the angle of depression to its base as 3º. How tall isthe multistorey building?

Answer 1

The height of the building = 36.51 m

Step-by-step explanation:

The distance from the John's apartment to the multistorey building = 80m

To better understand this question, we will be using an illustration:

To get the height of the building, we need to find x and y respectively:

x = distance from the position of John to the top of the building

y = distance from the position of John to the base of the building

To get x, we will apply tangent ratio (TOA):

opposite = x

adjacent = 80 m

angle = 22°

`\begin{gathered} \tan \text{ 22}\degree\text{ = }(opposite)/(adjacent) \\ \tan \text{ 22}\degree\text{ = }(x)/(80) \\ x\text{ = 80(tan 22}\degree)\text{ = 80}(0.4040) \\ x\text{ = 32.32 m} \end{gathered}`

To get y, we will apply tangent ratio (TOA):

opposite = y

adjacent 80m

angle = 3°

`\begin{gathered} \tan 3\degree\text{ = }(opposite)/(adjacent) \\ \tan 3\degree\text{ = }(y)/(80) \\ y\text{ = 80(tan 3}\degree)\text{ = 80(0.0524)} \\ y\text{ = 4.19 m} \end{gathered}`

The height of the building = x + y

The height of the building = 32.32 + 4.19

The height of the building = 36.51 m