A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of tree is 66 degrees. Determine the height of the tree, to the nearest foot.
45
a tree casts a 12 f shadow at the same time a 10ft flagpol case a 20ft shadow how tall is the tree
42
24ft
To determine the height of the tree, we can use trigonometry and specifically the tangent function. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the opposite side is the height of the tree and the adjacent side is the length of the shadow. Let's label the height of the tree as "h" and the length of the shadow as "s".
We know that the length of the shadow is 20 feet and the angle of elevation is 66 degrees.
Using the tangent function, we have:
tan(angle) = opposite/adjacent
Plugging in the values, we get:
tan(66) = h/20
To find the height of the tree, we need to isolate "h". Rearranging the equation, we have:
h = tan(66) * 20
Now, we can calculate the height of the tree using a scientific calculator or a trigonometric table.
h ≈ tan(66) * 20
h ≈ 2.365 * 20
h ≈ 47.3 feet
Therefore, the height of the tree is approximately 47.3 feet, rounded to the nearest foot.