Question

An inquisitive math student is standing 25 feet from the base of the Washington Monument. The angle of elevation from her horizontal line of sight is 87.4°. If her “eye height” is 5ft, how tall is the monument?Help please!

Answer 1

From the given figure, we can see a right triangle of base 25 feet

An acute angle of measure 87.4 degrees

We need to find the opposite side to this angle, then we will use

tan (x) = opposite side/adjacent side

The opposite side is the height from the eyes of the student to the top of the Monument

The adjacent side is 25 feet

`\because\tan (87.4)=(h)/(25)`

Multiply both sides by 25 to find h

`\begin{gathered} \therefore h=25*\tan (87.4) \\ \therefore h=550.54275 \end{gathered}`

Round it to 2 decimal places

∴ h = 550.54 feet

Add the height of the girl to it to find the height of the Monument

∴ The height of the Monument = 550.54 + 5 = 555.54 feet

∴ The tall of the monument is 555.54 feet