This is a perfect place to use Pythagoras' rule. When you do that, the answer rolls out immediately, and if you don't catch it , it falls off the edge of the desk.
Pythagoras' Theorem:
In a RIGHT triangle, the square of the longest side is equal to
(one short side)² + (other short side)² .
This is EXACTLY what you need, because MLN is a RIGHT triangle, you know the length of both sort sides, and you need to find the length of the longest side.
M = 5 , M² = 25 L = 12 , L² = 144
Add the squares together: 25 + 144 = 169
Pythagoras says that 169 is the square of N .
When you take its square root, you'll have the length of 'N'.
The tangent ratio is tan(38°) = opposite/adjacent = (height of cliff)/(distance to base) Multiplying the equation by the denominator gives height of cliff = (80 ft)*tan(38°) ≈ 62.5 ft
