From an observation deck, Matt spots two deer to the right of the observation deck, standing 108 feet apart in a field below. The angles of depression to each of the deer are 15o20’ and 36o17’. How high is the observation deck he is standing on?

The height of the observation deck is approximately 47.266 feet.

Step-by-step explanation:

We include a geometrical representation of the statement in the image attached below. Let be O the location of the observation deck, and A and B the locations of the two deers, which are 108 feet apart of each other. By knowing that sum of internal angles within triangle equals 180º. The angles O, B and A are now determined:

(1)

By the law of Sine we determine the length of the segment OB:

(2)

If we know that , and , then the length of the segment OB is:

Lastly, we determine the height of the observation deck by the following trigonometric identity:

(3)

If we know that and , then the height of the observation deck is:

The height of the observation deck is approximately 47.266 feet.

a

b

d

step-by-step explanation:

step-by-step explanation:

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