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## What Is Angle of Elevation?

**Angle of Elevation Definition:** Let us first define Angle of Elevation. Let O and P be two points such that the point P is at higher level. Let OA and PB be horizontal lines through O and P respectively. If an observer is at O and the point P is the object under consideration, then the line OP is called the line of sight of the point P and the angle AOP, between the line of sight and the horizontal line OA, is known as the angle of elevation of point P as seen from O. If an observer is at P and the object under consideration is at O, then the angle BPO is known as the angle of depression of O as seen from P.

**Angle of elevation formula:** The formula we use for angle elevation is also known as altitude angle. We can measure the angle of the sun in relation to a right angle using angle elevation.Horizon Line drawn from measurement angle to the sun in right angle is elevation.Using opposite, hypotenuse, and adjacent in a right triangle we can find finding the angle elevation. From right triangle sin is opposite divided by hypotenuse; cosine is adjacent divided by hypotenuse; tangent is opposite divided by adjacent. To understand angle of the elevation we will take some

Angle of elevation problems. Suppose if a tower height is 100 sqrt(3) metres given. And we have to find angle elevation if its top from a point 100 metres away from its foot. So let us first collect information, we know height of tower given is 100sqrt3, and distance from the foot of tower is 100 m. Let us take (theta) be the angle elevation of the top of the tower…we will use the trigonometric ratio containing base and perpendicular. Such a ratio is tangent. Using tangent in right triangle we have,

tan (theta) = perpendicular / adjacent

tan (theta) = 100sqrt(3)/100 = sqrt(3).

tan (theta) = tan 60

theta = 60 degree.

Hence, the angle elevation will be 60 degree

**Example: **The elevation angle of the top of the tower from a point on the ground, which is 30 metre away from the foot of the tower, is 30 degree. Find the height of the tower.

**Solution: **Let AB be the top A of tower height h metres and C be a point on ground such that the angle elevation from the top A of tower AB is of 30 degree.

In triangle ABC we are given angle C = 30 degree and base BC = 30 m and we have to find perpendicular AB. So, we use those trigonometrically ratios which contain base and perpendicular. Clearly, such ratio is tangent. So, we take tangent of angle C.

In triangle ABC, taking tangent of angle C, we have

tan C = AB/AC

tan 30 = AB/AC

1/sqrt(3) = h/30

h = 30/sqrt(3) metres = 10 sqrt(3) metres.

Hence, the height of the tower is 10 sqrt(3) metres.

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