A nest is 15 meters high in a tree. From it's nest, a bird flies 17 meters to the ground to reach a leaf. How far is the leaf from the base of the tree?

Answer: the leaf is 8m from the base of the tree.

Step-by-step explanation:

Assuming the bird flew along a straight line from the nest to the the leaf on the ground, then a right angle triangle is formed. The distance flown by the bird represents the hypotenuse of the right angle triangle. The vertical distance of the nest from the ground represents the opposite side of the triangle. The distance of the leaf, h from the base of the tree represents the adjacent side of the triangle.

Therefore, to find the distance, h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

17² = 15² + h²

289 = 225 + h²

h² = 289 - 225 = 64

h = √64

h = 8m

the leaf is 8 meters away from the tree

Step-by-step explanation:

we can think of this problem as a right triangle where height represents a leg, and what flew the bird represents the hypotenuse

then we would have to find the other leg

for this we can use Pythagoras

h = hypotenuse = 17 meters

l1 = leg1 = 15 meters

l2 = leg2 = ?

h² = l1² + l2²

17² = 15² + l2²

17² - 15² = l2²

289 - 225 = l2²

64 = l2²

√64 = l2

8 = l2

the leaf is 8 meters away from the tree