To answer this question, we will use the following diagram as reference:
To determine h, we will use the Pythagorean theorem. Recall that the Pythagorean theorem states that:

where a and b are the lengths of the legs of a right triangle and c is the hypotenuse length.
Therefore:

Solving the above equation for h, we get:
![h=\sqrt[]{196ft^2-9ft^2}.](https://img.qammunity.org/2023/formulas/mathematics/college/naxj88ub2ewexwk0nodp5gtg77vg7hymhu.png)
Simplifying the above result, we get:
![h=\sqrt[]{187}ft.](https://img.qammunity.org/2023/formulas/mathematics/college/5qzqoo98xd6ov3z0imeo70gczt9lna70kc.png)
Answer:
![h=\sqrt[]{187}ft\approx3.6979ft\text{.}](https://img.qammunity.org/2023/formulas/mathematics/college/66zbi5eewqncwofx4pwve91qcghnl6ccju.png)