Respuesta :
Answer
The estimated height of the monument = 40.18 ft.
Explanation
The question asks us to estimate the height of the monument, given that the monument's shadow is 22.5 ft long.
And that Calvin has a height of 6.25 ft and a shadow length of 3.5 ft.
All of these measurements, taken at the same exact time of 1:30 pm.
That the measurements were taken at the same time indicates that the position of the Sun (which is what causes the shadows), is the same for the two shadow measurements.
Thus allowing us to treat the two cases as two similar triangles. We can then write a similar triangle relationship that
[tex]\frac{Length\text{ of the monument's shadow}}{Actual\text{ height of the monument}}=\frac{Length\text{ of Calvin's shadow}}{\text{ Calvin's height}}[/tex]Let the Actual height of the monument be x.
Length of the monument's shadow = 22.5 ft.
Length of Calvin's shadow = 3.5 ft.
Calvin's Height = 6.25 ft.
So, we can substitute these, and obtain
[tex]\begin{gathered} \frac{22.5}{x}=\frac{3.5}{6.25} \\ \text{Cross Multiply} \\ x\times3.5=22.5\times6.25 \\ 3.5x=140.625 \\ \text{Divide both sides by 3.5} \\ \frac{3.5x}{3.5}=\frac{140.625}{3.5} \\ x=40.17857=40.18\text{ ft.} \end{gathered}[/tex]Hence, the estimated height of the monument = 40.18 ft.
Hope this Helps!!!
