Geometry Word problem involving the Pythagorean Theorem The length of a shadow of a bullding is $10 \mathrm{~m}$. The distance from the top of the building to the tip of the shadow is $26 \mathrm{~m}$. Find the height of the building. If necessary, round your answer to the nearest tenth.

Step 1 ：Given that the length of the shadow of a building is 10 meters and the distance from the top of the building to the tip of the shadow is 26 meters.

Step 2 ：We can use the Pythagorean theorem to find the height of the building. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as: \(a^2 + b^2 = c^2\)

Step 3 ：In this case, the length of the shadow is one side of the triangle (let's call it \(a\)), the height of the building is the other side (let's call it \(b\)), and the distance from the top of the building to the tip of the shadow is the hypotenuse (let's call it \(c\)).

Step 4 ：We can rearrange the Pythagorean theorem to solve for \(b\): \(b = \sqrt{c^2 - a^2}\)

Step 5 ：Substituting the given values into the equation gives: \(b = \sqrt{26^2 - 10^2}\)

Step 6 ：Calculating the above expression gives the height of the building as 24.0 meters.

Step 7 ：Final Answer: The height of the building is \(\boxed{24.0}\) meters.