I really need a step by step explanation on this problem please.

Question

A surveyor wishes to determine the height of a building. The transit is positioned on level land at a distance of 160 feet from the foot of the building. An angle of 41 degrees 30' is read in sighting the top of the building. The height from the ground to the transit telescope is 5.5 feet. What is the height of the building?

Answer 1

You can make a sketch that shows the height of the transit to be 5.5 ft from the ground and 160 ft from the building. The total height, H, of the building will be the height of building from the top of the transit, h, plus the 5.5 ft of the transits' height: H = h + 5.5.

To find h, we can see that we have a right triangle with a 41.5 degree (30 mins = .5 degrees) angle from the transit to the top of the building of height, h, and a perpendicular distance of 160 ft from the transit to the building. Therefore, we can figure out h by knowing that tan(41.5°) = h/160--->h = 160tan(41.5°)--->h ≅ 141.56. Putting this value into our earlier equation, H = h + 5.5, we can determine that the total height of the building is H = 141.56 + 5.5--->H ≅ 147 ft.

Hope this helps!

Answer 2

Draw and label a diagram!

A represents the top of the transit

B represents the top of the building

C represents the point on the building 100' from the transit

The height of the building is BC + 5.5

BC / 100 = tan 41° 30'

BC = 100 tan 41° 30'

Can you solve for BC and answer?