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How to Find Height and Distance using Trignometry?

Trigonometry has a wide range of practical applications, including the measurement of heights and distances between objects. One of the most common applications of trigonometry is to determine the distance between two or more points or to find the height of an object or the angle it subtends from a given point.

The following are the main definitions that are used when finding heights and distances:

1. Line of Sight 2. Angle of Elevation 3. Angle of Depression

What is Line of Sight?

The line of sight is the line that is drawn from the observer's eyes to the point being viewed on the object. It represents the direct path that light takes from the object to the observer's eye and is used to determine visibility and perspective in visual perception.

What is Angle of Elevation?

The angle of elevation is the angle between a horizontal line and a line of sight to an object above the horizontal. It is used to determine the height or distance of an object and is measured in degrees.

For example, when you look up at a tall building from a distance. The angle between the ground and your line of sight to the top of the building is the angle of elevation.

What is Angle of Depression?

The angle of depression is the angle between a horizontal line and a line of sight to an object below the horizontal. It is used to determine the depth or distance of an object and is measured in degrees.

For example, if someone is standing on top of a hill and looking down at a car parked at the bottom of the hill, the angle of depression would be the angle formed between the horizon and the line of sight to the car.

How to Measure Angle with a Clinometer?

A clinometer is an instrument that is used to measure the angle of slope, inclination or elevation of an object.

What are Trigonometric Ratios?

Trigonometric ratios are mathematical expressions that relate the sides of a right triangle to its angles.

What are the 6 trigonometric ratios?

Trigonometric ratios are mathematical relationships that describe the ratios of the lengths of sides in a triangle. These ratios are specifically applicable to right triangles, where one angle measures 90^{o}. There are 3 primary trignometric ratios namely sine, cosine, and tangent whereas it also encompasses three other ratios such as secant, cosecant and cotangent. These ratios, commonly abbreviated as sin, cos, tan, sec, cosec and cot, respectively, represent the relationships between the sides of a right triangle and the angles within it. By knowing the measure of an acute angle, denoted as θ, one can calculate the values of these trigonometric ratios for the given triangle.

Trignometric Ratios Table

The table provided can assist in solving height and distance problems by utilizing trigonometric ratios.

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