Question

The sun causes a flagpole to cast a shadow that measures 85 ft. from the base of the pole. At the same time of the day, a 6.5 ft. tall basketball player casts a shadow that measures 9.75 ft.

The basketball player’s little sister is 3.5 ft. tall. At the same time of the day, determine her shadow’s length to the nearest tenth of a foot.

Answer 1

Length of the shadow of player's sister is 5.25 feet.

Explanation:

From the figure attached,

AB represents the basketball player and DE is his little sister.

Height of basketball player = 6.5 ft

Length of shadow of the player = 9.75 ft

Height of player's sister = 3.5 ft

Since, ΔABC and ΔEDC are the similar triangles, their corresponding sides will be proportional.

`(AB)/(DE)= (ED)/(DC)`

`(6.5)/(3.5)= (9.75)/(x)`

x =
`(9.75* 3.5)/(6.5)`

x = 5.25 ft

Therefore, length of the shadow of player's sister is 5.25 feet.