A fighter plane observes a target on the ground with an angle of depression of 21 degrees. The target is 3.5 miles away along a direct line of sight. How high is the fighter plane? Round to hundredths.
Please help!
h/3.5 = sin 21°
so you'd take sin or 21 and then multiply that by 3.5, to get h, right?
I did that and I got 1.25 when rounded. Is that right?
That's what I get. Good work.
To find the height of the fighter plane, we can use trigonometry.
Let's assume that the height of the fighter plane is h miles. The angle of depression is the angle formed between the line of sight from the fighter plane to the target and the horizontal line. In this case, the angle of depression is given as 21 degrees.
We can use the tangent function to find the height of the fighter plane. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is h and the adjacent side is the distance to the target, which is 3.5 miles.
So we have the equation: tan(21 degrees) = h / 3.5
To find h, we can rearrange the equation and solve for h:
h = 3.5 * tan(21 degrees)
Using a scientific calculator, we can find that tan(21 degrees) is approximately 0.3841. Multiplying this by 3.5 gives us the height of the fighter plane:
h = 3.5 * 0.3841 ≈ 1.3444 miles
Therefore, the height of the fighter plane is approximately 1.34 miles.