The angle of depression from D to F measures 25°. If EF = 10 yd, find DE
To find DE, we need to use trigonometry, specifically the tangent function.
First, let's understand what the angle of depression is. The angle of depression is the angle formed between a horizontal line and the line of sight while looking downwards. In this case, the angle of depression from D to F measures 25°. This means that if you were standing at point D and looked down towards point F, the angle formed between the horizontal and your line of sight is 25°.
We're given that EF = 10 yd. Let's assume that the distance between D and F is x yd.
Now, consider right triangle DEF. We have the opposite side (EF = 10 yd) and we want to find the adjacent side (DE = ?).
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side:
tan(angle) = opposite/adjacent
In this case, tan(25°) = EF/DE
Plugging in the known values, we get:
tan(25°) = 10/DE
To find DE, we rearrange the formula:
DE = 10 / tan(25°)
Now, we can use a calculator to find the value of DE:
DE ≈ 21.47 yd
Therefore, DE is approximately 21.47 yards.
time to draw a diagram and review your basic trig functions:
DE/10 = tan 25°
It also helps to recall the alternate interior angles between parallel lines are equal.