# Find A Formula For A B Illustrated By These Examples What Is Angle of Elevation?

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## What Is Angle of Elevation?

Definition of angle of elevation: Let’s first define the angle of elevation. Let O and P be two points such that point P is at a 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 the line of sight to the point P and the angle AOP is the line between the line of sight and the horizontal line OA. Angle of elevation of point P as seen from O. If an observer is at P and the object under consideration is at O, the angle BPO is known as the angle of depression of O as seen from P.

Angle of Height Formula: The formula we use for angle height is also known as height angle. We can measure the Sun’s angle relative to a right angle by using angular altitude. A horizon line drawn at right angles from the measuring angle to the sun is the altitude. Using opposites, hypotenuses, and sides in right triangles, we can find angles. height From a right-angled triangle sin is divided oppositely by the hypotenuse; The cosine divided by the hypotenuse is the tangent divided by the opposite side. We will take something to understand the angle of elevation

Angle of Elevation Problems. Suppose if the height of the tower is 100 square meters (3) meters. And we have to find the angular height if its top is from a point 100 meters away from its feet. So let’s collect the information first, we know the height of the tower is 100sqrt3, and the distance from the foot of the tower is 100m. Let the angular height of the top of the tower be (theta)…we will use the base and perpendicular trigonometric ratio. Such a ratio is tangent. Using the tangent to a right triangle,

tan (theta) = perpendicular / adjacent

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

tan (theta) = tan 60

theta = 60 degrees.

Therefore, the angle height will be 60 degrees

Example: The angle of elevation of the top of the tower from a point on the ground 30 meters from the foot of the tower is 30 degrees. Find the height of the tower.

Solution: Let AB be the top A of the tower height h meters and let C be a point on the ground such that the angle height from the top A of the tower AB is 30 degrees.

In triangle ABC we are given angle C = 30 degrees and base BC = 30 m and we have to find the perpendicular AB. So, we use those trigonometric ratios that have a base and a perpendicular. Clearly, such a ratio is tangent. So, we take the tangent of angle C.

In triangle ABC, taking the tangent to angle C, we have

Tan C = AB/AC

Tan 30 = AB/AC

1/sqrt(3) = h/30

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

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

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