The mirror is 5 feet in front of him and is approximately 40 feet from the base of the mountain. ∆ Jackson is 6’4” tall. Approximately how high is the top of the mountain.
Draw a sketch to illustrate the process and be sure to use mathematical language to show and explain your work.

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MrRoyal MrRoyal · Answer 1 · 2022-01-14T15:28:14+01:00

The height of the top of the mountain is 50.67 feet

Jackson placing the mirror in front of him will result in relations that have equivalent ratios.

So, the equivalent ratios are represented as:

[tex]5\ ft : 40 \ ft= 6'4" : x[/tex]

Where x represents the height of the mountain

Cancel out the common units

[tex]5 : 40= 6'4" : x[/tex]

Express as fractions

[tex]\frac{5 }{ 40}= \frac{6'4" }{ x}[/tex]

Make x the subject

[tex]x = 6'4" \times \frac{40}{5}[/tex]

[tex]x = 6'4" \times 8[/tex]

Multiply

[tex]x = 48'\ 32"[/tex]

Convert the unit to feet

[tex]x = 48' + \frac{32}{12}'[/tex]

[tex]x = 48' + 2.67'[/tex]

[tex]x = 50.67'[/tex]

Hence, the height of the top of the mountain is 50.67 feet

Read more about equivalent ratios at:

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