Helen stands 66 m away from the base of the tree. If the line of sight makes an angle of 30 with the top of the tree with respect to the horizon. What is the height (h) of the tree?

h= 66 root 3 or 66 multiplied by the sq. root of 3.

first turn this into a triangle...

the base is 66 and you know two of the angles (30 deg. and 90 deg (the base and the ground)). Now this is a 30-60-90 triangle. the rules 4 30-60-90 is the base is x, the hyp. is 2x and the other leg is x multiplied by the sq. root of 3. you know x (66) so your answer is 66 multiplied by the sq. root of 3

To find the height (h) of the tree, we can use trigonometry. We have a right triangle formed by the line of sight, the distance from Helen to the base of the tree, and the height of the tree.

In this case, we can use the tangent function because we have the opposite side (h) and the adjacent side (66 m). The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.

So, we can use the following formula:

tan(theta) = opposite/adjacent

In this case, the angle theta is 30 degrees, the opposite side is h (the height of the tree), and the adjacent side is 66 m.

tan(30) = h/66

To find the value of tan(30), we can use a calculator or refer to a trigonometric table. The tangent of 30 degrees is approximately 0.577.

So, we have:

0.577 = h/66

Now, we can solve this equation for h by multiplying both sides by 66:

0.577 * 66 = h

h ≈ 38.1

Therefore, the height of the tree (h) is approximately 38.1 meters.