Question

A gardener stands 30 feet away from a tree,making an angle of elevation of 42 degrees from the top of the gardener’s head to the top of the tree.if the gardener is 5 feet tall ,how tall is the tree to the nearest foot

Answer 1

If the gardener head of the top of the tree . If the gardener is 5 feet tall , the answer is 7 '6 feet tall

Answer 2

To find the height of the tree, use the tangent function and set up a right triangle. The height of the tree is approximately 27 feet.

Step-by-step explanation:

To find the height of the tree, we can use the tangent function and set up a right triangle. Let's call the height of the tree 'h'.

Since the gardener is 5 feet tall and the angle of elevation is 42 degrees, the opposite side of the triangle is h - 5 (the difference between the height of the tree and the height of the gardener). The adjacent side is the distance from the gardener to the tree, which is 30 feet.

Using the tangent function, we have tan(42) = (h - 5) / 30. Solving for h, we get h = 30 * tan(42) + 5.

Plugging in the values, we have h = 30 * 0.9004040408 + 5 = 27.012121224.

Rounding to the nearest foot, the height of the tree is approximately 27 feet.