two observers P and Q, 75 metres apart observes a kite (k) in the same vertical plane from the same side of the kite. The angle of elevation of the kote from P and Q are 35° and 95° respectively find the height of the kite to the nearest metre?
To find the height of the kite, we can use the concept of trigonometry and the given information of the angles of elevation and the distance between the observers.
Let's denote the height of the kite as 'h'. We need to find the value of 'h' to the nearest metre.
We can use the tangent function to relate the angles of elevation with the height of the kite:
For observer P:
tan(35°) = h / x
where x is the distance between observer P and the kite.
For observer Q:
tan(95°) = h / (x + 75)
where x + 75 is the distance between observer Q and the kite, since they are 75 metres apart.
We can rearrange both equations to solve for 'h'.
For observer P:
h = x * tan(35°)
For observer Q:
h = (x + 75) * tan(95°)
Now, we can equate the two equations to find 'x':
x * tan(35°) = (x + 75) * tan(95°)
Solve this equation to find the value of 'x'. Once we find 'x', we can substitute it back into either of the equations to find the height 'h' of the kite to the nearest metre.
The angle of elevation cannot be greater than 90°.
I guess you could think of such an angle, but in that case the observer would be looking back over his shoulder.
Suppose you fix the typo, and then note that if the two angles are x and y, with x < y, and the height of the kit is h, then draw a diagram and you can see that
h cotx - h coty = 75
so,
h = 75/(cotx-coty)