Im not sure where i went wrong with this question

Question

Question: From the top of a cliff 112 m high, the angle of depression to a boat is 9°15′. How far is the boat from the foot of the cliff?

I tried doing this:

cos(9 degrees 15 minutes) = 112/x

x * cos(9 degrees 15 mins) = 112

x = 112/cos(9 degrees 15 mins)

and yet i get 113 m...

The answer is 600-something apparently, don't know where I'm going wrong. Please help!

Answer 1

-----

|\ß

| \

| \

112 \

| \

|---x---boat

Angle of depression is ß as shown in the figure.

tanß = height/distance = 112/x

Or x =112/tan(9 degree15 min) =687.7

i.e. boat is 687.7 m away from the foot of the cliff

Answer 2

Hi Sam,

Using cosine (cos) would give you the ratio of the adjacent side to the hypotenuse. You have used 112 as the adjacent measure and x as the hypotenuse. Since the angle given is the angle below the horizontal, the distance from the base of the cliff, x, should be the adjacent side and 112 should be the opposite side. Thus you need a tangent (tan) function.

You should set it up with:

tan(9 deg 15 min) = 112/x and solve for x the same way you did. Doing it that way I get about 688 feet.