Question

a 33-m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 36 m. find the length of the shadow. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify Pythagorean theorem

We have a right triangle where:

• Leg 1 (building height): $a = 33$ m
• Hypotenuse (top to shadow tip): $c = 36$ m
• Leg 2 (shadow length, unknown): $b$

The theorem is $a^2 + b^2 = c^2$, rearranged to $b = \sqrt{c^2 - a^2}$

Step2: Calculate squared values

$c^2 = 36^2 = 1296$, $a^2 = 33^2 = 1089$

Step3: Compute difference

$c^2 - a^2 = 1296 - 1089 = 207$

Step4: Find square root, round

$b = \sqrt{207} \approx 14.4$

Answer:

14.4 m