Answer:
h = 11.2
Step-by-step explanation:
Let point M' be a point on AM that is 5 units toward point A from M. Let point B lie on AM such that KB⊥AM. Let x = AB; then BM' = 15 -x. The Pythagorean theorem gives rise to two equations in x and h:
- x² + h² = AK² = 13²
- (15-x)² + h² = M'K² = 14²
Subtracting the first from the second gives ...
(225 -30x +x² + h²) - (x² + h²) = 196 -169
225 -30x = 27
x = 198/30 = 6.6
Then ...
h = √(13² -x²) = √(169 -43.56) = √125.44
h = 11.2
