If the cliff is vertical, how can there be a ledge? And how can the angle looking down be other than 90 degrees?
I don't get it.
A climber, working his way up a vertical cliff stops for a rest on the ledge. The ledge where he stopped is 12 meters wude. The angle of depression from the edge of the ledge to the bottom of the cliff is 72 degree and the angle of elevation to the top of the cliff is 88 degree. Find the height of the cliff.
2 answers
It appears that the situation looks like a shelf sticking out from a vertical wall. The shelf is 12m wide, so we have two right triangles:
Looking down, from shelf height h, we have
h/12 = tan 72
Looking up to the peak at height p above the shelf, we have
p/12 = tan 88
The total cliff elevation is h+p
Looking down, from shelf height h, we have
h/12 = tan 72
Looking up to the peak at height p above the shelf, we have
p/12 = tan 88
The total cliff elevation is h+p
2 answers