A tree casts a shadow 50 yards long when the angle of the sun (measured from the
horizon) is 30 degree. How tall is the tree in feet?
(A) 150p3 (B) 50p3 (C) 150 (D) 75p3 (E) None of the above.
50yds = 150 ft.
150tan30 = 150*sqrt3/3 = 50sqrt3 = 50p3
150
To solve this problem, we can use trigonometry. The length of the shadow of the tree is the adjacent side of a right triangle, and the height of the tree is the opposite side. We can use the tangent function to find the height of the tree.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, we have the tangent of 30 degrees equal to the height of the tree divided by the length of the shadow.
Let's solve for the height of the tree:
tan(30 degrees) = height of the tree / length of the shadow
In the given problem, the length of the shadow is 50 yards, and we need to find the height of the tree. Let's substitute the values into the equation:
tan(30 degrees) = height of the tree / 50
To find the height of the tree, we can multiply both sides of the equation by 50:
height of the tree = 50 * tan(30 degrees)
Using a calculator, we can find the value of tan(30 degrees) which is approximately 0.5774:
height of the tree = 50 * 0.5774
height of the tree ≈ 28.87 yards
Now, we need to convert the height of the tree from yards to feet. Since there are 3 feet in 1 yard, we can multiply the height of the tree by 3:
height of the tree in feet = 28.87 yards * 3 feet/yard
height of the tree in feet ≈ 86.61 feet
So, the height of the tree is approximately 86.61 feet.
None of the answer choices (A) 150p3, (B) 50p3, (C) 150, (D) 75p3, (E) None of the above, match the calculated height of the tree.