Answer:
The height of the building is approximately 18 meters.
Step-by-step explanation:
The question is:
FROM THE HIGH PART OF A WALL OF 8M HEIGHT, YOU CAN SEE THE LOW AND HIGH PART OF A BUILDING WITH ELEVATION AND DEPRESSION ANGLES OF 37° AND 45° RESPECTIVELY. CALCULATE THE HEIGHT OF THE BUILDING A.18 B.14 C.12 D.24 E.16
Solution:
Consider the diagram below.
Consider the triangle ABC.
Compute the value of y as follows:
[tex]tan\ 37^{o}=\frac{AB}{BC}[/tex]
[tex]0.754=\frac{8}{y}[/tex]
[tex]y=\frac{8}{0.754}[/tex]
[tex]=10.61\\\approx 11[/tex]
Thus, the length of side AD is also 11 meters.
Now consider the triangle AED.
Compute the value of x as follows:
[tex]tan\ 45^{o}=\frac{AE}{ED}[/tex]
[tex]1=\frac{11}{x}[/tex]
[tex]x=11[/tex]
Then the height of the building is:
[tex]\text{Height of the Building}=x+8[/tex]
[tex]=11+8\\=19[/tex]
From the options provided it can be concluded that the height of the building is approximately 18 meters.
