A man looks up at the top of a tree. The angle of elevation is 42 degrees. If the tree is 20 feet tall, which of the following best represents the distance from the base of the tree where the man is standing?
You can not copy and paste so I do not see your choices but
tan E = 20/d
d = 20/tan E
To determine the distance from the base of the tree where the man is standing, we can use trigonometry. In this case, we have the height of the tree and the angle of elevation.
Let's assume the distance from the base of the tree to the man is represented by 'x'.
By using the tangent function, we can set up the following equation:
tan(42 degrees) = opposite / adjacent
In this scenario, the opposite side is the height of the tree (20 ft) and the adjacent side is the distance 'x' from the base of the tree to the man.
tan(42 degrees) = 20 ft / x
To solve for 'x', we can rearrange the equation:
x = 20 ft / tan(42 degrees)
Using a calculator, we can find the value of 'x':
x ≈ 20 ft / tan(42 degrees)
x ≈ 20 ft / 0.9004 (rounded to four decimal places)
x ≈ 22.20 ft
Therefore, the distance from the base of the tree where the man is standing is approximately 22.20 feet.