Question

the tree in jacobs yard casts a shadow that is 27 feet long. jacob is 5 feet tall and casts a shadow that is 4.5 feet long. the two triangles formed are similar because the angle to the sun is the same. what is the height of the tree? 24.3 feet 26.5 feet 27.5 feet 30 feet

Explanation:

Step1: Set up proportion for similar triangles

Let \( h \) be the height of the tree. Since the triangles are similar, the ratios of corresponding sides are equal. So we have \(\frac{h}{27}=\frac{5}{4.5}\).

Step2: Solve for \( h \)

Cross - multiply: \( 4.5h = 5\times27 \). First, calculate \( 5\times27 = 135 \). Then, \( h=\frac{135}{4.5} \). Dividing 135 by 4.5 gives \( h = 30 \).

Answer:

30 feet