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: Identify Pythagorean theorem

Let shadow length = $x$, building height $a=34$, hypotenuse $c=37$. Use $c^2=a^2+x^2$.

Step2: Rearrange for shadow length

$x=\sqrt{c^2-a^2}$

Step3: Substitute values

$x=\sqrt{37^2-34^2}=\sqrt{1369-1156}=\sqrt{213}$

Step4: Calculate and round

$\sqrt{213}\approx14.6$

Answer:

14.6 m