Question

From the observation deck of a skyscraper, Meena measures a 45 angle of
depression to a ship in the harbor below. If the observation deck is 862 feet high,
what is the horizontal distance from the base of the skyscraper out to the ship?
Round your answer to the nearest tenth of a foot if necessary.

Answer 1

Answer: 1145 ft

Step-by-step explanation:

tan 45=1145/x

x tan45/1=1145

x tan 45/ tan 45= 1145/ tan 45

x= 1145/ tan45= 1145... ≈1145

Answer 2

The horizontal distance from the base of the skyscraper will be "862 feet".

Given values are:

Angle of depression,

• 45°

Observation deck length,

• 914 feet high

As we know,

→ $tan \theta = \frac{Opposite \ side}{Adjacent \ side}$

or,

→ $tan 45^{\circ} = \frac{Observation \ deck \ length}{Horizontal \ distance}$

hence,

→ $Horizontal \ distance = Observation \ deck \ length\times tan 45^{\circ}$

By substituting the given values, we get

→                                   $= 862\times 1$

→                                   $= 862 \ feet$

Thus the answer above is the correct one.

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