# Thread: finding the height of the cliff

1. ## finding the height of the cliff

From the top of the cliff an observer spots two ships out at sea. One is north east with an angle of depression of 6 ° while the other is south east with an angle of depression of 4 °. If the two ships are 200m apart, find the height of the cliff, to the nearest metre.

by a long method of calculaions i got 350.92 = 351m.
is this correct??
is there an easier way to do it??

2. If we call the height of the light house x, then the distance from ground level to each of the boats is:

$xtan(86)$ and $xtan(84)$

However we know the angel between the boats is 90 degrees since one is NE and one is SE. So we can apply the Pythagorean theorem:

$(xtan(86))^2 + (xtan(84))^2 = 200^2$

Solve for x, should be the height of the light house.

See this picture: (By the way, in the water view, the bottom line isn't necessarily a full line. Check the top view for a clearer view)

3. ok
so should i get to

h^2 = (200^2) / (tan^2(86) + tan^2(84))

then just type in calculator and get
135.58m
= 136m

4. Correct.

5. ok awesome
thanks heaps

6. do i need to take the sqrt of that???