Question

A hummingbird's nest is 6 meters high in a tree and a flower is on the ground 4 meters away from the base of the tree. How far will the hummingbird need to fly to get from its nest to the flower? if necessary round to the nearest tenth.

Answer 1

Answer:

7.2 metres

Step-by-step explanation:

For this problem, it's best to draw a diagram to help you visualize. See below for a diagram. I used H for hummingbird; T for tree, F for flower. We are looking for "t", the blue side.

Label sides using the opposite angle's letter, but use its lowercase.

Since this is a right triangle and we know two of the three sides, use the Pythagorean Theorem. The general formula is:

a² + b² = c²

"c" means the hypotenuse, or the longest side. "a" and "b" are the other non-hypotenuse sides, called 'legs'.

In this problem, our legs are f = 6 and h = 4. The hypotenuse is "t".

Write the formula and solve for "t".

h² + f² = t²                Substitute the values f = 6 and h = 4

4² + 6² = t²              Square the numbers

16 + 36 = t²             Add

52 = t²                Put the variable on the left side as standard format

t = √52              Square root both sides

t ≈ 7.2                 Rounded answer

Remember to add in the units.

t = 7.2 m

Therefore, the hummingbird will need to fly 7.2 metres to get from its nest to the flower.