Question

King Kong stands on the edge of the roof of a 62 foot high building. You poke your head out of a manhole and measure the angles of elevation to the top of King Kong's head and to his feet as 55 degrees and 53.1 degrees respectively.
How far is your manhole from the building?
____ feet
How tall is King Kong?
____ feet

Answer 1

Answer:

46.55 feet (approx).

4.48 feet ( approx )

Step-by-step explanation:

Let x be distance manhole from the building. ( in feet ) and y be the height of the King Kong.

∵ The angles of elevation to the top of King Kong's head and to his feet are 55 degrees and 53.1 degrees respectively.

By the trigonometric ratio,

$\tan 53.1^{\circ}=\frac{62}{y}$

$\implies y =\frac{62}{\tan 53.1^{\circ}}\approx 46.55$

Thus, the distance of the manhole from the building would be 46.55 feet (approx).

Again by the trigonometric ratio,

$\tan 55^{\circ}=\frac{62+x}{46.55}$

$\tan 55^{\circ}\times 46.55=62 + x$

$66.48 = 62 + x$

$\implies x = 66.48 - 62 = 4.48$

Hence, King Kong is approximately 4.48 feet long.