Question

Chase is admiring a statue in Fairfax Park. The statue is 8.7 meters taller than he is, and Chase is standing 3.4 meters away. How far is it from the top of the statue to Chase's head? If necessary, round to the nearest tenth.

meters

Answer 1

To determine the distance from the top of the statue to Chase's head, we need to calculate the height difference and the horizontal distance to form a right triangle.

1. Let \( h \) be Chase's height in meters.
2. The height of the statue is \( h + 8.7 \) meters.
3. Chase is standing 3.4 meters away from the base of the statue.

The vertical distance from Chase's head to the top of the statue is:

\[
\text{Height of statue} - \text{Chase's height} = (h + 8.7) - h = 8.7 \text{ meters}
\]

Next, we apply the Pythagorean theorem to find the direct distance from the top of the statue to Chase's head:

\[
d = \sqrt{(8.7)^2 + (3.4)^2}
\]

Calculating each squared value:

\[
(8.7)^2 = 75.69
\]
\[
(3.4)^2 = 11.56
\]

Now, add these:

\[
75.69 + 11.56 = 87.25
\]

Now take the square root:

\[
d = \sqrt{87.25} \approx 9.34
\]

Rounding to the nearest tenth, the distance from the top of the statue to Chase's head is approximately:

\[
\boxed{9.3} \text{ meters}
\]