Hello there. To solve this question, we have to apply the pythagorean theorem.
A 25.5 foot ladder rests against the side of a house at a point 24.1 above the ground. The foot of the ladder is x feet from the house.
We want to find the value of x with 1 decimal place
First, remember the pythagorean theorem: Given a right triangle with sides A, B and C, it is true that:
In this case, the length of the ladder is the hypotenuse of the triangle and the height the ladder is against the house above the ground is one of the sides.
Then, we perform:
[tex]25.5^2=24.1^2+x^2[/tex]
Subtract 24.1² on both sides of the equation
[tex]25.5^{2}-24.1^{2}=x^{2}[/tex]
Rewrite the expression in the left hand side as:
a² - b² = (a - b)(a + b)
[tex]\begin{gathered} (25.5-24.1)(25.5+24.1)=x^{2} \\ 1.4\cdot49.6=x^{2} \\ 69.44=x^{2} \end{gathered}[/tex]
Take the square root on both sides of the equation
[tex]x\approx8.3[/tex]
