Trigonometry Question..?

Question

Two boats are 500m apart, they're both in sight of a clifftop. 15 Degree and 24 degrees, how do you find the total length to the bottom of the cliff?

Two boats are 500m apart, and in line with a cliff. One boat is looking up at an angle to the top of the cliff at 15 degrees and the other at 24. What is the height of the cliff?

Sorry for the edit, I made an error with what I was finding.

Answer 1

let the height of cliff be h
then
distance of first ship =x
distance of first ship =x+500
now
1.h/x=tan 24
2.h/(x+500)=tan 15
from 1
x=hcot24
from 2
x=hcot15-500
therefore
h(cot15-cot24)=500
h=336.47

Answer 2

the cliff is going to be the same height for both boats = y
one boat is x meters from the cliff and is at a 24 degree angle to the top of the cliff
the second boat is 500m + the distance of the first boat (x) from the cliff and is at a 15 degree angle to the top of the cliff

now you have 2 equations:
boat 1
tan(24degrees) = y / x

boat 2
tan(15degrees) = y / (500+x)

solve for y for the first boat
y = x * tan(24degrees)

take y and plug it into the second boat equation

tan(15degrees) = (x * tan(24degrees)) / (500+x)
tan(15degrees) = 0.2679
tan(24degrees) = 0.4452

now solve for x
0.2679 = (x * 0.4452) / (500+x)

0.2679(500+x) = 0.4452x
133.95 + 0.2679x = 0.4452x
133.95 = 0.4452x - 0.2679x
133.95 = 0.1773x
x = 755.50m
boat 1 is 755.50meters from the cliff

take this and plug it back into the equation for boat 1
tan(24degrees) = y / 755.50m
tan(24degrees) = 0.4452

0.4452 = y / 755.50
0.4452 (755.50) = y
336.35 = y

the cliff is 336.35 meters

Answer 3

stan(24) = h = (s + 500)tan(15)
stan(24) = stan(15) + 500tan(15)
s(tan(24) - tan(15)) = 500tan(15)
s = 500tan(15)/(tan(24) - tan(15))
s = 756 m
s + 500 = 1,256 m