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jon is in a raft that is 117m from the base of a 56m cliff. what is the angle of depression from the top of the cliff to the raft?

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You can form a right-angled triangle from the base of the cliff to the raft (this is the opposite side to an angle), the base of the cliff to the top of the cliff (this is the adjacent side to an angle), and the top of the cliff to the raft (this is the hypotenuse of the triangle).

We know the value of the adjacent and opposite side, so we can use the trigonometric function 'tan' to work out an angle that we can find the angle of depression from.

90 minus the angle that you can work out from this will be equal to the angle of depression.

So if the angle of depression is called x, then:

Tan(90 - x) = O/A

O is the length of the opposite side of the triangle and A is the adjacent side (both have been mentioned before).

Sub in values:

Tan(90 - x) = 117/56

Rearrange for x:

90 - x = Arctan(117/56)

Therefore x = 90 - arctan(117/56)

x = 25.6 degrees to 1 decimal place.
User Mike Zavarello
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