Question

ellen is admiring a statue in winchester park from 5 meters away. if the distance between the top of the statue to ellens head is 9 meters, how much taller is the statue than ellen? if necessary, round to the nearest tenth.
______ meters

Explanation:

Step1: Identify right triangle sides

We have a right triangle where one leg is the horizontal distance ($a = 5$ m), the hypotenuse is the distance between the top of the statue and Ellen's head ($c = 9$ m), and the other leg $b$ is the height difference we need to find.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^2 + b^2 = c^2$. Rearrange to solve for $b$:
$$b = \sqrt{c^2 - a^2}$$

Step3: Substitute values and calculate

Substitute $a=5$, $c=9$:
$$b = \sqrt{9^2 - 5^2} = \sqrt{81 - 25} = \sqrt{56} \approx 7.5$$

Answer:

7.5 meters