Question

The angle of elevation from an observer to the bottom edge of the Delaware River drawbridge observation deck located 200 feet from the observer is 30 degrees. The angle of elevation from the observer to the top of the observation deck is 40 degrees. How tall is the chimney above the floor of the observation deck, to the nearest tenth of a foot

Answer 1

The height of the chimney above the floor of the observation deck is 52.4 ft

Two right angle triangle will be formed.

Right angle triangle:

Right angle triangle are triangle that has one of its angle as 90 degrees.

Therefore, using trigonometric ratio,

adjacent side = distance of observer from the bottom edge of the Delaware River drawbridge observation deck

Therefore,

tan 40 = opposite / adjacent

Where

x = height of the observer to the top of the observation deck

tan 40 = x / 200

x = 200 tan 40

x = 167.819926235

x = 167.82 ft

tan 30 = opposite / adjacent

y = height of the observer to the bottom of the observation deck

tan 30 = y / 200

y = 200 tan 30

y = 115.470053838

y = 115.47 ft

The height of the chimney above the floor of the observation deck = height of the observer to the top of the observation deck - height of the observer to the bottom of the observation deck

The height of the chimney above the floor of the observation deck = 167.82 - 115.47 = 52.35 ft

learn more on trigonometric ratio here: brainly.com/question/23854119