xzavierguerrero7
contestada

To estimate the height of a stone figure, Anya holds a small square up to her eyes and walks backwards from the figure. She stops when the bottom of the figure aligns with the bottom edge of the square and the top of the figure aligns with the top edge of the square. Her eye level is 1.84 m from the ground. She is 3.50 m from the figure. What is the height of the figure to the nearest hundredth of a meter?


A.8.50 m

B.4.38 m

C.6.65 m

D.2.45 m

Respuesta :

8.50 m is the height of the figure to the nearest hundredth of a meter.

Answer: Option A

Step-by-step explanation:

So from the figure we have,

Angle CBA = Angle DBA  = 90 degree

Angle CAB = Angle ADB  = 90 degree

Angle CAB = Angle BDA = 90 degree

Now using the similar triangle properties and Pythagorean theorem,

             [tex]\frac{B A}{B D}=\frac{B C}{A B}[/tex]

            [tex]B C=\frac{(A B)^{2}}{B D}[/tex]

          [tex]B C=\frac{(B D)^{2}+(A D)^{2}}{B D}[/tex]

           [tex]B C=\frac{(3.5)^{2}+(1.84)^{2}}{1.84}[/tex]

          [tex]B C=\frac{12.25+3.3856}{1.84}=\frac{15.6356}{1.84}=8.497=8.5 \mathrm{m}(\text {approximately})[/tex]

Ver imagen jacknjill
MrRoyal

The height of the figure is 8.50 meters

To calculate the height of the figure, we make use of the following equivalent ratios

[tex]BA : BD = BC : BA[/tex]

Express the ratio, as a fraction

[tex]\frac{BA}{BD} = \frac{BC}{BA}[/tex]

Make BC, the subject of the formula

[tex]BC = \frac{BA * BA}{BD}[/tex]

Substitute known values, in the above equation

[tex]BC = \frac{BA * BA}{1.84}[/tex]

This gives

[tex]BC = \frac{BA^2}{1.84}[/tex]

By Pythagoras theorem, we have:

[tex]BC = \frac{BD^2 + AD^2}{1.84}[/tex]

So, we have:

[tex]BC = \frac{1.84^2 + 3.50^2}{1.84}[/tex]

Evaluate

[tex]BC = 8.50[/tex]

Hence, the height of the figure is 8.50 meters

Read more about Pythagoras theorem at:

https://brainly.com/question/654982

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