Answer:
A tower is 1964 feet tall. The angle of elevation from the base of an office building to the top of the tower is 37 degrees. The angle of elevation from the roof of the office building to the top of the tower is 19 degrees.
A) how far away is the office building from the tower? Assume the side of the tower is vertical.
B) how tall is the office building?
Please draw a sketch and explain.
Distance between the tower and the building is 1479.98 ft and the height of the office building is of 1454.41 ft.
Step-by-step explanation:
Given:
Height of the vertical tower = 1964 ft
From the office building:
Angle of elevation from the base (office) to the top of the tower = 37°
Angle of elevation from the roof (office) to the top of the tower = 19°
Using trigonometric ratios:
Tan(∅) = Opposite/ Adjacent
From the diagram shown we have assumed that the distance between the office building and the tower is "x" ft
And the height of the office building to be "y" ft
Let find the x values from triangle MNO :
⇒ [tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
⇒ [tex]tan(37)=\frac{1964}{x}[/tex]
⇒ [tex]x=tan(37)\times 1964[/tex]
⇒ [tex]x=1479.98[/tex] ft ....equation (i)
Now,
In triangle PQN.
⇒ [tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
⇒ [tex]tan(19)=\frac{1960-y}{x}[/tex]
⇒ [tex]tan(19)=\frac{1960-y}{1479.98}[/tex] ...x = 1479.98 from equation (i)
⇒ [tex]1964-y=tan(19)\times 1479.98[/tex]
⇒ [tex]1964-y=509.59[/tex]
⇒ [tex]1964-509.59=y[/tex] ...subtracting 509.79 and adding y on both sides
⇒ [tex]1454.41=y[/tex]
Height of the office building = 1454.41 ft.
Distance between the tower and the building is 1479.98 ft and the height of the office building is of 1454.41 ft.
