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Solved Problems

Home >> Trigonometry Ratios >> Find Height, Distance using T  Ratios >> Angle of Elevation >> Angle of Elevation and find Height & Distance
Before you study this topic you should know what is angle of elevation and depression:
What is Angle of Elevation ?
The formulas we used in angle of elevation :
To find height and distance we use Tan θ = Opposite Side / Adjacent Side
To find length or hypotenuse we use Sin θ = Opposite Side / Hypotenuse
Example 1 : A person is standing 5m away from tree, the angle of elevation of the top of tree is 60° find the height of tree ?
Solution : Let AB is the tree. B is the foot and A is the top of tree. C is the point on the ground where the person is standing and which is making the angle of elevation of 60°
If we draw a picture it will look like as below 
so we get
CB (Distance from tree) = 5m
∠BCA = 60°
Right angle is at point B
AB (Height) = ?
A right angle triangle △ ABC is formed in which
AB is the Opposite Side from angle of elevation
BC is the Adjacent Side from angle of elevation
We know that Tan θ = Opposite Side / Adjacent Side
Value of √ 3 is 1.73 so,
AB = 5 x 1.73 = 8.65
AB = 8.65m is the height of tree
Example 2 :Height of tree is 8.65m, the angle of elevation of the top of tree is 60° find the distance at which the person is standing away from tree ?
Solution : Let AB is the tree. B is the foot and A is the top of tree. C is the point on the ground where the person is standing and which is making the angle of elevation of 60°
If we draw a picture it will look like as below 
so we get
CB (Distance from tree) = ?
∠BCA = 60°
Right angle is at point B
AB (Height) = 8.65m
A right angle triangle △ ABC is formed in which
AB is the Opposite Side from angle of elevation
BC is the Adjacent Side from angle of elevation
We know that Tan θ = Opposite Side / Adjacent Side
Value of √ 3 is 1.73 so,
8.65 = CB x 1.73
CB = 8.65 / 1.73
CB = 5
so the person is standing 5m away from the tree
Example 3 : A tree is 5m high. If angle of elevation is 45° find the hypotenuse
Let AB is the tree. B is the foot and A is the top of tree. C is the point on the ground where a person is standing and which the angle of elevation of 45°
If we draw a picture it will look like as below 
so we get
AC = ?
∠ BCA = 45°
AB = 5m
A right angle triangle △ ABC is formed in which
AB is the Opposite Side from angle of elevation
AC is the Hypotenuse Side
We know that Sin θ = Opposite Side / Hypotenuse
AC = 5 x √ 2
Value of √ 2 is 1.41 so,
5 x 1.41 = 7.05
AC = 7.05m is the hypotenuse
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