Some Applications of Trigonometry — Practice Quiz
Gujarat Board · Class 10 · Mathematics
Try a 4-question quiz on Some Applications of Trigonometry for Gujarat Board Class 10 Mathematics: tap an answer to check it and see why.
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Quick Quiz: Some Applications of Trigonometry
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A ladder 10 meters long is placed against a wall such that it makes an angle of 30° with the ground. What is the height at which the ladder touches the wall?
From a point 20 meters away from the base of a tower, the angle of elevation to the top is 45°. What is the height of the tower?
A boy is flying a kite at a height of 30 meters. If the string makes an angle of 60° with the horizontal, what is the length of the string?
A tree casts a shadow of 15 meters when the angle of elevation of the sun is 30°. What is the height of the tree?
Sample Questions
Which of the following are correct statements about angles of elevation and depression? (Select all that apply)
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Angle of elevation is formed when we look upward, Angle of depression is formed when we look downward, Both angles are measured from the horizontal
Angle of elevation occurs when looking above horizontal level, angle of depression when looking below. Both are measured from the horizontal reference line. There's no fixed relationship between their magnitudes, and the line of sight changes direction based on the viewing angle.
From the top of a building 50 meters high, the angle of depression to a car on the road is 30°. How far is the car from the base of the building?
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50√3 meters
Using tan θ = opposite/adjacent. For angle of depression, tan 30° = 50/distance. Since tan 30° = 1/√3, we get distance = 50/(1/√3) = 50√3 meters.
If sin θ = 3/5, what is the value of tan θ?
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3/4
If sin θ = 3/5, then opposite = 3 and hypotenuse = 5. Using Pythagoras theorem: adjacent = √(5² - 3²) = √(25 - 9) = √16 = 4. Therefore, tan θ = opposite/adjacent = 3/4.
The angle of elevation of the top of a tower from two points at distances 4m and 9m from the base are complementary. If the height of the tower is 6m, what are these angles?
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tan⁻¹(3/2) and tan⁻¹(2/3)
From 4m: tan α = 6/4 = 3/2, so α = tan⁻¹(3/2). From 9m: tan β = 6/9 = 2/3, so β = tan⁻¹(2/3). Since tan α × tan β = (3/2) × (2/3) = 1, the angles are complementary (α + β = 90°).
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