Question

a 33-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: Identify the triangle type

This is a right triangle, with the building height (33 m) as one leg, the shadow length (\(x\)) as the other leg, and the distance from the top of the building to the tip of the shadow (38 m) as the hypotenuse. We can use the Pythagorean theorem, which states that for a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 33\), \(c=38\), and we need to find \(b=x\).

Step2: Apply the Pythagorean theorem

Rearrange the formula to solve for \(x\): \(x=\sqrt{c^{2}-a^{2}}\). Substitute \(a = 33\) and \(c = 38\) into the formula: \(x=\sqrt{38^{2}-33^{2}}\). First, calculate \(38^{2}=1444\) and \(33^{2} = 1089\). Then, \(38^{2}-33^{2}=1444 - 1089=355\). So, \(x=\sqrt{355}\approx18.8\) (rounded to the nearest tenth).

Answer:

\(18.8\)