Heights and Distances
Trigonometry has practical applications in measuring heights and distances that cannot be measured directly. This is one of the most important applications of trigonometric ratios.
Key Concepts
Height of an Object
Example: Height of a Building
Distance Between Two Objects
Example: Distance to a Tower
Two Object Problem
Example: Height of a Flagstaff on a Tower
Level Ground Problems
Example: Distance Between Two Boats
Practice Problems
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From a point m from a building, the angle of elevation to the top is . Find the height of the building.
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From the top of a m tower, the angle of depression to a car is . Find the distance of the car from the base of the tower.
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Two towers are m apart. From the top of the first tower (height m), the angle of depression to the top of the second tower is . Find the height of the second tower.
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From a ship, the angle of elevation to the top of a lighthouse is . After sailing m towards the lighthouse, the angle becomes . Find the height of the lighthouse.