Question

Kimberly is admiring a statue in Newberry Park from 4 meters away. If the distance between the top of the statue to Kimberly's head is 9 meters, how much taller is the statue than Kimberly? If necessary, round to the nearest tenth.

Answer 1

Explanation:

To solve this problem, we need to use the concept of similar triangles.

Let's draw a diagram to visualize the situation:

* Statue top

|

|

| 9 m

|

|

|

/ \

/ \ 4 m

Kimberly

We can see that we have two right triangles, one formed by Kimberly, the ground, and the point where the statue touches the ground, and the other formed by the statue, the ground, and the point where Kimberly's head touches the ground.

These two triangles are similar because they have the same angles. In particular, the angle at Kimberly's eye is the same as the angle at the top of the statue. This means that the corresponding sides are proportional.

Let's call the height of the statue "h". Then, we have:

h/9 = (h+4)/4

We can solve for "h" by cross-multiplying:

4h = 9(h+4)

4h = 9h + 36

5h = 36

h = 7.2

Therefore, the height of the statue is 7.2 meters. To find out how much taller the statue is than Kimberly, we subtract their heights:

7.2 m - 1.5 m = 5.7 m

So the statue is 5.7 meters taller than Kimberly.