Download the Problem of Hight and Distance Trigonometry MCQs with Free PDF for PPSC, FPSC, PMS, NTS, KPKPSC, and SPSC exam
Height and distance trigonometry is a branch of trigonometry that deals with the calculation of the height and distance of objects. It is used in many different fields, such as surveying, engineering, and navigation.
The main trigonometric ratios used in height and distance trigonometry are the sine, cosine, and tangent. The sine of an angle is the ratio of the opposite side to the hypotenuse of a right triangle. The cosine of an angle is the ratio of the adjacent side to the hypotenuse of a right triangle. The tangent of an angle is the ratio of the opposite side to the adjacent side of a right triangle.
To calculate the height of an object using trigonometry, we need to know the angle of elevation to the top of the object, the distance to the object, and the sine of the angle of elevation. The angle of elevation is the angle between the horizontal line and the line of sight to the top of the object.
The formula for calculating the height of an object using trigonometry is:
Height = Distance × Sine of Angle of Elevation
For example, if the angle of elevation to the top of a building is 30 degrees, the distance to the building is 100 meters, and the sine of 30 degrees is 0.5, then the height of the building is:
Height = 100 meters × 0.5 = 50 meters
To calculate the distance to an object using trigonometry, we need to know the height of the object, the angle of elevation to the top of the object, and the tangent of the angle of elevation.
The formula for calculating the distance to an object using trigonometry is:
Distance = Height × Tangent of Angle of Elevation
For example, if the height of a building is 50 meters, the angle of elevation to the top of the building is 30 degrees, and the tangent of 30 degrees is 0.577, then the distance to the building is:
Distance = 50 meters × 0.577 = 28.85 meters
Height and distance trigonometry is a powerful tool that can be used to solve many different problems. It is a fundamental concept in many different fields, and it is essential for anyone who wants to understand the relationship between height and distance.
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