the angle of depression from D to F measures 40 degrees. If EF= 14 yd, find DE. round answer to nearest 10th
tan40 = EF/DE,
tan40 = 14/DE,
DE = 14 / tan40 = 16.7 yds.
To find DE, we can use the trigonometric function tangent.
Tangent is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the angle of depression is from D to F, so DE is the side adjacent to the angle, and EF is the side opposite the angle.
The tangent of an angle can be calculated using the formula:
tan(angle) = opposite / adjacent
In this case, we have:
tan(40 degrees) = EF / DE
Now we solve for DE:
DE = EF / tan(40 degrees)
Since EF = 14 yd, we substitute that value into the equation:
DE = 14 / tan(40 degrees)
Using a calculator, we calculate the tangent of 40 degrees and divide 14 by that value:
DE ≈ 14 / 0.8391
Finally, we round the answer to the nearest tenth:
DE ≈ 16.7
Therefore, DE ≈ 16.7 yd.
To find DE, we can start by drawing a diagram.
Let's assume that point D is above point F, and DE is the horizontal distance between points D and E. The angle of depression from D to F is 40 degrees.
Given that EF = 14 yd, we need to find DE.
In a right triangle DEF, with angle DFE measuring 90 degrees, we can use tangent function to find DE.
Tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is EF and the adjacent side is DE.
So, we have:
tan(40°) = EF / DE
Rearranging the equation to solve for DE, we get:
DE = EF / tan(40°)
Plugging in the values, we have:
DE = 14 / tan(40°)
Using a calculator, we find:
DE ≈ 14 / 0.8391 ≈ 16.7 yd
Therefore, DE is approximately 16.7 yd (rounded to the nearest tenth).