Question

a 34-m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 37 m. find the length of the shadow. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let shadow length = $x$. The building, shadow, and line form a right triangle, so $x^2 + 34^2 = 37^2$.

Step2: Calculate squared values

$34^2 = 1156$, $37^2 = 1369$. Substitute: $x^2 = 1369 - 1156$

Step3: Solve for $x^2$

$x^2 = 213$

Step4: Find square root, round

$x = \sqrt{213} \approx 14.6$

Answer:

14.6 m