# math help

posted by on .

What is the distance Y Z in metres between the boat and the bouy, to 2 significant figures?
A surveyor, standing at an observation point on a cliff top of a height 300m above sea level, can see a boat and a bouy out at sea, both directly in front of him. He measures the angle from the top of the cliff to the bouy Y as 27 degrees and the angle from the top of the cliff to the boat Z as 18 degrees

make a diagram and put in all your information.
You should see two right-angled triangles.

tan 27 = 300/x, where x is the distance from the base of the cliff to the bouy is your first calculation.

if y is the distance from the base of the cliff to the boat, then tan 18 = 300/y

evaluate x and y, take y-x and state the answer to 2 significant figures.
Let me know what you get.

Reiny thank you so much for helping me.
Is it 55 ??

no, from tan 27 = 300/x
I got x= 300/tan27 = 588.8

from tan 18 = 300/y I got
y=300/tan 18 = 923.3

then the difference is 923.3-588.8
=334.5
which is 330 m to 2 significant figures.