Applications of Trigonometry
Telangana Board · Class 10 · Mathematics
Flashcards for Applications of Trigonometry — Telangana Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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A boy sees the top of a pole at an angle of elevation of 60° from a point 8 m away from the foot of the pole. Find the height of the pole.
Answer
Step 1: Use tan 60° = AB/OB. Step 2: Here, OB = 8 m and AB = height of pole = h. Step 3: tan 60° = h/8. Step 4: √3 = h/8. Step 5: h = 8√3 m. Answer: The height of the pole is 8√3 m.
From a helicopter, Rajender observes a person on the ground at an angle of depression of 45°. If the helicopter is 500 m high, find the distance of the person from Rajender.
Answer
Step 1: Use sin 45° = OA/OB. Step 2: OA = 500 m and OB = distance from the person to Rajender = x. Step 3: sin 45° = 500/x. Step 4: 1/√2 = 500/x. Step 5: x = 500√2 m. Answer: The distance is 500√2 m.
A tower stands vertically on the ground. From a point 15 m away from its foot, the angle of elevation of the top is 45°. Find the height of the tower.
Answer
Step 1: Use tan 45° = opposite/adjacent. Step 2: tan 45° = height/15. Step 3: 1 = height/15. Step 4: height = 15 m. Answer: The height of the tower is 15 m.
A tree was broken in a storm and the top touches the ground making a 30° angle with the ground. The distance between the foot of the tree and the point where the top touches the ground is 6 m. Find th
Answer
Step 1: Form a right triangle with the broken part. Step 2: Use tan 30° = opposite/adjacent. Step 3: tan 30° = height of the standing part / 6. Step 4: 1/√3 = height/6. Step 5: height of the standing …
A ladder of length x m leans against a wall making an angle of 60° with the ground. What trigonometric ratio is most useful to find the height reached by the ladder, and why?
Answer
Use sine. Step 1: The ladder is the hypotenuse. Step 2: The height reached on the wall is the opposite side. Step 3: Sine connects opposite and hypotenuse. Step 4: If the angle is 60°, then sin 60° = …
Why is the angle of elevation measured with the horizontal line and not with the vertical line?
Answer
The angle of elevation is the angle between the line of sight and the horizontal when the object is above eye level. This keeps the reference line the same in every problem, so triangles can be formed…
A boy observes the top of a pole at 60° from a point 8 m away. Find the height using the tangent ratio.
Answer
Step 1: Identify opposite side = height of pole = h. Step 2: Identify adjacent side = 8 m. Step 3: tan 60° = h/8. Step 4: √3 = h/8. Step 5: h = 8√3 m. Answer: 8√3 m.
A person on the ground is seen from a helicopter at an angle of depression of 45°. If the helicopter height is 500 m, find the distance from the helicopter to the person.
Answer
Step 1: Use the right triangle formed by the helicopter, the ground person, and the vertical height. Step 2: Use sin 45° = opposite/hypotenuse. Step 3: 1/√2 = 500/x. Step 4: x = 500√2 m. Answer: 500√2…
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