Question

the length of a shadow of a building is 27 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: Use Pythagorean theorem

We have a right - triangle where the height of the building is one leg ($a = 27$m) and the length of the shadow is the other leg ($b = 38$m). The distance from the top of the building to the tip of the shadow is the hypotenuse $c$. The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$.

Step2: Substitute values

Substitute $a = 27$ and $b = 38$ into the formula: $c=\sqrt{27^{2}+38^{2}}=\sqrt{729 + 1444}=\sqrt{2173}$.

Step3: Calculate the value

$\sqrt{2173}\approx46.6$. Rounding to the nearest tenth, we get $46.6$m.

Answer:

$46.6$m