Question

a 35 - m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 38 m. find the length of the shadow. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

We have a right - triangle where the two legs are the height of the building ($a = 35$ m) and the length of the shadow ($b = 38$ 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 $a = 35$ and $b = 38$ into the formula: $c=\sqrt{35^{2}+38^{2}}=\sqrt{1225 + 1444}=\sqrt{2669}$.

Step3: Calculate the square - root

$\sqrt{2669}\approx51.66$.

Step4: Round to the nearest tenth

Rounding $51.66$ to the nearest tenth gives $51.7$.

Answer:

$51.7$ m