The angle of elevation of X from Y is 30 degree.if |XY|=40m, how high is X above the level of Y?
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draw a diagram and review your basic trig functions. You can see that if the height is h, then
h/40 = sin30°
To find the height of X above the level of Y, we can use trigonometric functions.
Let's denote the height of X above the level of Y as h.
In a right-angled triangle, the opposite side of the angle of elevation is the height (h), and the hypotenuse is the distance (|XY|).
In this case, the angle of elevation is 30 degrees, and the distance |XY| is 40 meters.
Using the trigonometric function tangent (tan), we can write:
tan(angle) = opposite/adjacent
tan(30 degrees) = h/40 meters
Now we can solve for h:
h = tan(30 degrees) * 40 meters
Using a calculator or trigonometric table, we find that tan(30 degrees) is approximately 0.5774.
Substituting this value into the equation, we have:
h = 0.5774 * 40 meters
Calculating this multiplication, we find:
h ≈ 23.1 meters
Therefore, X is approximately 23.1 meters above the level of Y.
To find the height of X above the level of Y, we can use the trigonometric relationship between the angle of elevation and the opposite side of a right triangle.
In this case, the height of X above the level of Y is the opposite side, and the distance XY (the hypotenuse) is given as 40m. The angle of elevation, 30 degrees, is the angle between the hypotenuse and the ground level.
To calculate the height, we can use the sine function because it relates the opposite side (height) and the hypotenuse:
sin(angle) = opposite/hypotenuse
sin(30) = height/40
To isolate the height, we can rearrange the equation:
height = sin(30) * 40
Now, we can solve for the height:
height = 0.5 * 40
height = 20m
Therefore, X is 20 meters above the level of Y.