From a point 45 meters above level ground, a surveyor measures the angle of depression of an object on the ground at 68°. Approximate the distance from the object to the point on the ground directly beneath the surveyor. (Round your answer to two decimal places.)

Well, draw a triangle! I mean, they only gave you two pieces of information. Can't see any way to use it?

At the top of the cliff is point A. At the bottom of the cliff is point B. AB = 45m. Somewhere out along the ground is point C.

Now, angle BAC is 68deg.
BC/45 = tan(68)
BC = 45 tan(68) = 45 * 2.475 = 111.38m

To solve this problem, we can use trigonometry.

The angle of depression is the angle between the horizontal level and the line of sight downward to the object. In this case, the angle of depression is 68°.

We are given that the surveyor is at a height of 45 meters above the ground. Let's call the distance from the surveyor to the object "x."

To find the distance from the object to the point on the ground directly beneath the surveyor, we need to find the length of the base of the right triangle formed by the surveyor's position, the object, and the point on the ground.

Since the angle of depression is given and we have the opposite side (the height difference), we can use the tangent function:

tan(angle) = opposite / adjacent

tan(68°) = 45 / x

To isolate x, we can rearrange the equation:

x = 45 / tan(68°)

Now we can calculate the value of x:

x = 45 / tan(68°)

Using a scientific calculator, we find:

x ≈ 21.09 meters

Therefore, the distance from the object to the point on the ground directly beneath the surveyor is approximately 21.09 meters.

Hint: tan = height/width

ok, would you be able to set up for me?

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