Stanely is 6ft tall. He wants to stand in the shade of a tree that is 35ft tall. If the tree casts a 10ft shadow, what is the farthest Stanely can stand from the tree and be completely in its shadow? Round your answer to nearest tenth of a roof?
8.3
8.28... OR APPROXIMATLY 8.3
if he stands at distance d, his shadow will be 10-d, so
35/10 = 6/(10-d)
d = 58/7
To find the farthest distance Stanley can stand from the tree and be completely in its shadow, we can use similar triangles. Let's call the distance from Stanley to the tree as "x".
We have two similar triangles: one formed by the tree, its shadow, and the ground, and another formed by Stanley, his shadow, and the ground.
The ratio of the height of the tree to the length of its shadow is the same as the ratio of Stanley's height to the length of his shadow:
Tree height / Tree shadow = Stanley height / Stanley shadow
Since we know the tree height (35ft), the tree shadow (10ft), and Stanley's height (6ft), we can set up the following equation:
35ft / 10ft = 6ft / x
To solve for x (the distance Stanley can stand from the tree), we can cross-multiply:
35ft * x = 10ft * 6ft
x = (10ft * 6ft) / 35ft
x ≈ 1.7143 ft (rounded to the nearest tenth)
Therefore, the farthest Stanley can stand from the tree and be completely in its shadow is approximately 1.7 feet.