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.
What is the scale factor relating the height of the ball player to his shadow’s length?
To find the scale factor relating the height of the basketball player to the length of their shadow, we need to divide the height of the basketball player by the length of their shadow.
Let's denote the height of the basketball player as h and the length of their shadow as s.
Given:
Height of the basketball player (h) = 6.5 ft.
Length of the basketball player's shadow (s) = 9.75 ft.
The scale factor (k) is given by:
k = h / s
Plugging in the values:
k = 6.5 ft. / 9.75 ft. = 0.6666667
Therefore, the scale factor relating the height of the basketball player to the length of their shadow is approximately 0.6667.
h/85 = 6.5/9.75
h =