A tower is 1964 feet tall. The angle of elevation from the base of an office building to the top of the tower is 37degrees. The angle of elevation from the roof of the office building to the top of the tower is 19degrees.

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 :

⇒

⇒

⇒

⇒ ft   ....equation (i)

Now,

In triangle PQN.

⇒

⇒

⇒               ...x = 1479.98 from equation (i)

⇒

⇒

⇒          ...subtracting 509.79 and adding y on both sides

⇒  

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.

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.