Question

What is the height of the tree in the image below? 10 points Wall 4 6 ft 24 O I foot O 36 foot None of the above

Answer 1

16 ft

Step-by-step explanation

Step 1

because the ligth comes in the same angle, we have 2 similar triangles .

so,as the triangles are similar,the ratio of the shorter leg to the bigger leg must be equal.

`\begin{gathered} ratio=\frac{shorter\text{ leg}}{\text{bigger leg}} \\ ratio1=ratio2 \\ (h)/(24)=(4)/(6) \end{gathered}`

Step 2

solve for h

`\begin{gathered} (h)/(24)=(4)/(6) \\ \text{cross multiply} \\ 6\cdot h=4\cdot24 \\ 6h=96 \\ \text{divide boths} \\ (6h)/(6)=(96)/(6) \\ h=16 \end{gathered}`

therefore, the heigth of the tree is 16 ft