when an airplane is 800m above the ground its angle of elevation from a point p on ground is 30°.How far is the plane from p by line of sight
answer
sin30 = opposite which is height / hypotenuse which is line of sight distance
but we all know sin 30 = 1/2
so
2 times 800
To find the distance between point P and the airplane by line of sight, you can use trigonometry. The given information tells us that the airplane is 800m above the ground and the angle of elevation from point P is 30°.
We can consider a right triangle, where the height of the triangle is the distance between the airplane and the ground (800m) and the angle of elevation is the angle opposite the height. The distance between point P and the airplane is the hypotenuse of this triangle.
Now, we can use trigonometric ratios to find the required distance. In this case, we can use the sine ratio.
The sine of an angle in a right triangle is equal to the length of the opposite side divided by the length of the hypotenuse.
So, let's call the distance between point P and the airplane "d".
sin(30°) = 800m / d
To find the value of sin(30°), we can use a calculator or refer to trigonometric tables. The sin(30°) is equal to 0.5.
0.5 = 800m / d
To solve for "d," we can rearrange the equation:
d = 800m / 0.5
d = 1,600m
Therefore, the distance between point P and the airplane by line of sight is 1,600 meters.
Well, if the airplane is 800m above the ground and its angle of elevation from point P is 30 degrees, we can use some trigonometry to find the distance.
First, we need to find the height of the triangle formed by the airplane, point P, and the vertical line from the airplane to the ground. This can be calculated using the formula: height = opposite side x tan(angle). In this case, the opposite side is 800m and the angle is 30 degrees.
So, height = 800m x tan(30 degrees) = 800m x 0.577 = 461.6m.
Now, we have a right-angled triangle with the height (opposite side) as 461.6m, and we need to find the adjacent side (distance from point P to the airplane). We can use the formula: adjacent side = opposite side / tan(angle).
Using the values we have, adjacent side = 461.6m / tan(30 degrees) = 461.6m / 0.577 = 800m.
So, the distance from point P to the airplane by line of sight is approximately 800m.
And that, my friend, is how geometry takes you to new heights! Oops, I meant distances!
To find the distance between point P and the airplane, we can use trigonometry. We'll use the tangent function since we have the angle of elevation.
Let's denote the distance between point P and the airplane as 'x'.
In a right triangle formed by the airplane, the height (800m) is the opposite side, and the distance 'x' is the adjacent side. The angle of elevation (30°) forms the acute angle between the opposite side and the hypotenuse.
Using the tangent function, we can write:
tan(30°) = opposite/adjacent
tan(30°) = 800/x
tan(30°) = (√3)/3 (approx)
Substituting the value of tangent in the equation:
(√3)/3 = 800/x
To solve for 'x', we can cross-multiply:
x = 800 * (3/√3)
x = 800 * (3/√3) * (√3/√3)
x = 800 * 3√3 / 3
x = 800√3 / 3
Simplifying further, we get:
x ≈ 462.27 meters
So, the airplane is approximately 462.27 meters away from point P by line of sight.