Question

Mark is vacationing out West. He wants to determine the height of a giant saguaro cactus. He stands 90 ft from the cactus so the tip of his shadow meets the tip of the cactus' shadow. If Mark is 6 ft tall and his shadow, s, is 7.0 ft long, what is the height, h, of the cactus? Round your answer to the nearest tenth of a foot if necessary.

Answer 1

The height of cactus is 83.1 feet.

Explanation:

Let the height of the cactus be represented by h. Given that the shadows of cactus and Mark meets at the same tip.

Then,

the distance from the cactus to the tip of its shadow = 90 ft + s

= 90 ft + 7 ft

= 97 feet

Thus comparing the two triangles, we have;

`(h)/(6)` =
`(97)/(s)`

`(h)/(6)` =
`(97)/(7)`

7 x h = 97 x 6

7h = 582

h =
`(582)/(7)`

= 83.1429

h = 83.1 feet

The height, h, of the cactus is 83.1 feet.