The length of a shadow of a building is $26 \mathrm{~m}$. The distance from the top of the bullding to the tip of the shadow is $35 \mathrm{~m}$. Find the height of the bullding. If necessary, round your answer to the nearest tenth.
Explanation
Recheck
2023 McGraw HilluC All Rights Reserved. Terms of Use

Step 1 ：This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of the shadow is one side of the triangle, the distance from the top of the building to the tip of the shadow is the hypotenuse, and the height of the building is the other side.

Step 2 ：We can use the Pythagorean theorem to solve for the height of the building. The formula is \(a^2 + b^2 = c^2\), where \(c\) is the length of the hypotenuse, \(a\) and \(b\) are the lengths of the other two sides.

Step 3 ：Given that the length of the shadow (\(a\)) is 26 meters and the distance from the top of the building to the tip of the shadow (\(c\)) is 35 meters, we can substitute these values into the formula: \((26)^2 + b^2 = (35)^2\).

Step 4 ：Solving for \(b\), we get \(b = \sqrt{(35)^2 - (26)^2}\).

Step 5 ：Calculating the above expression, we find that the height of the building (\(b\)) is approximately 23.4 meters.

Step 6 ：Final Answer: The height of the building is \(\boxed{23.4}\) meters.