Applications of Trigonometry — Practice Quiz
Telangana Board · Class 10 · Mathematics
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A boy observes the top of a tower at an angle of elevation of 60° from a point 10 meters away from the base. What is the height of the tower?
From the top of a 50m building, a person observes a car at an angle of depression of 30°. What is the distance of the car from the base of the building?
A ladder 10 meters long leans against a wall making an angle of 60° with the ground. What is the height reached on the wall?
The angle of elevation of the sun when a 6m pole casts a 6√3 m shadow is:
Sample Questions
Which trigonometric ratios are commonly used in height and distance problems? (Select all correct answers)
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sin θ, cos θ, tan θ
sin θ, cos θ, and tan θ are the primary ratios used. tan θ is most common for height-distance problems as it relates opposite to adjacent sides.
From a helicopter 300m above ground, a person is observed at 45° angle of depression. The horizontal distance to the person is:
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300 meters
Using tan 45° = height/distance. Since tan 45° = 1 and height = 300m, distance = 300/1 = 300 meters.
Which of these statements about angles of elevation and depression are true? (Select all correct)
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Angle of elevation is measured upward from horizontal, Angle of depression is measured downward from horizontal, Angle of depression from one point equals angle of elevation from the other
Angles of elevation and depression are measured from horizontal lines. They form alternate angles in parallel line geometry.
A tree is broken and bends to touch the ground at 30° angle, 8m from its base. The original height of the tree was:
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16 meters
Let the broken part be x meters. Using trigonometry: x cos 30° = remaining height, x sin 30° = 8. Solving: x = 16m, so original height = 16m.
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