Question

A math studentis standing 25 feet from the base of the washington manument. The angle of elevation from the horizontal line of sight is 87.4 degrees. If her eye height is at 5 feet how tall is the monument?

Answer 1

Answer:

$Height\ of\ monument=555.5\ ft$

Explanation:

$In\ the\ digram\ AC\ is\ the\ monument\ and\ DE\ is\ the\ student.\\\\AC=AB+BC\\\\Let\ AB=x\\\\BC=Height\ of\ the\ eye\ of\ the\ student=DE=5\ ft\\\\\Rightarrow AC=x+5.................................eq(1)\\\\Student\ is\ standing\ at\ a\ distance\ of\ 25\ ft.\\\\CD=25\ ft\\\\BE=CD=25\ ft\\\\Angle\ of\ elevation=87.4\textdegree\\\\\angle AEB=87.4\textdegree\\\\Now\ in\ \triangle ABE\\\\\tan \angle AEB=\frac{opposite}{adjacent}=\frac{AB}{BE}\\\\\tan 87.4=\frac{x}{25}\\\\x=25\times \tan 87.4$

$x=25\times 22.02171001\\\\x=550.54275\ ft\approx 550.5\ ft\\\\Height\ of\ monument=AC=x+5\\\\Height\ of\ monument=550.5+5\\\\Height\ of\ monument=555.5\ ft$