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.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b