The height of the building = 36.51 m
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°
[tex]\begin{gathered} \tan \text{ 22}\degree\text{ = }\frac{opposite}{adjacent} \\ \tan \text{ 22}\degree\text{ = }\frac{x}{80} \\ x\text{ = 80(tan 22}\degree)\text{ = 80}(0.4040) \\ x\text{ = 32.32 m} \end{gathered}[/tex]To get y, we will apply tangent ratio (TOA):
opposite = y
adjacent 80m
angle = 3°
[tex]\begin{gathered} \tan 3\degree\text{ = }\frac{opposite}{adjacent} \\ \tan 3\degree\text{ = }\frac{y}{80} \\ y\text{ = 80(tan 3}\degree)\text{ = 80(0.0524)} \\ y\text{ = 4.19 m} \end{gathered}[/tex]The height of the building = x + y
The height of the building = 32.32 + 4.19
The height of the building = 36.51 m
