Question

the length of a shadow of a building is 29 m. the distance from the top of the building to the tip of the shadow is 38 m. find the height of the building. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the triangle type

We have a right triangle, where the hypotenuse \( c = 38 \) m and one leg \( b = 29 \) m. We need to find the other leg \( a \) (height of the building).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \( a^{2}+b^{2}=c^{2} \). Rearranging for \( a \), we get \( a=\sqrt{c^{2}-b^{2}} \).

Step3: Substitute the values

Substitute \( c = 38 \) and \( b = 29 \) into the formula:
\( a=\sqrt{38^{2}-29^{2}}=\sqrt{(38 + 29)(38 - 29)}=\sqrt{67\times9}=\sqrt{603}\approx24.6 \) (rounded to the nearest tenth)

Answer:

\( 24.6 \) m