Step 1. Form a right triangle using the 25 ft length, h, and half of the horizontal length:
Step 2. Since the whole horizontal length is 48ft, half of it is equal to:
[tex]\frac{48ft}{2}=24ft[/tex]
Thus, we have that one leg of the triangle is h, and the other is 24 ft:
Step 3. The red triangle we have is a right triangle, and thus, we can use the Pythagorean theorem to find h.
The Pythagorean theorem for a right triangle is:
[tex](leg1)^2+(leg2)^2=(hypotenuse)^2[/tex]
In this case, the hypotenuse is the 25 ft length:
[tex]\text{hypotenuse}=25ft[/tex]
We will label the 24 ft length as leg 1, and h as leg 2:
[tex]\begin{gathered} \text{leg}1=24ft \\ \text{leg}2=h \end{gathered}[/tex]
Substituting in the Pythagorean theorem:
[tex](24ft)^2+h^2=(25ft)^2[/tex]
Step 4. Solve for h in the previous equation.
To solve for h, first, we solve the operations:
[tex]576^{}ft^2+h^2=625ft^2[/tex]
Subtract 576ft^2 to both sides:
[tex]\begin{gathered} h^2=625ft^2-576ft^2 \\ h^2=49ft^2 \end{gathered}[/tex]
Finally, take the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{h^2}=\sqrt[]{49ft^2} \\ h=7ft \end{gathered}[/tex]
We have found the answer for the value of h.
Answer:
[tex]h=7ft[/tex]
