Question

if your standing on the trail 220 feet from the bottom of the tree , you have to look up at 60 degree angle to see the top . how tall is the tree

Answer 1

The height of the tree can be calculated using the tangent of the 60 degree angle of elevation, which approximately equals to the height divided by 220 feet, leading to a height of approximately 380.64 feet.

Step-by-step explanation:

To determine the height of the tree when standing 220 feet from the base and looking up at a 60 degree angle, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the height and the distance from the object.

Here's the step-by-step process:

• Identify the right triangle formed by your line of sight and the distance from the base of the tree.
• Use the formula tan(60°) = height / 220 feet.
• Calculate the height by multiplying both sides by 220 feet to isolate the height variable.
• Since tan(60°) is approximately equal to √3 or about 1.732, the height calculation will be: height = 220 feet * 1.732

Therefore, the tree's height is approximately 380.64 feet.