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Answered on 06 Jan Learn Some Applications of Trigonometry

2. A bridge across the river makes an angle of 45 with the river bank. If the length of the bridge across... read more
2. A bridge across the river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, what is the width of the river? read less

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Answered on 06 Jan Learn Some Applications of Trigonometry

3. There is a small island in the middle of a 100 m wide river and a tall tree stands on the island.... read more
3. There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are the points directly opposite to each other on the two banks, and in a line with the tree. If the angles of elevation of the top of the tree from P and Q are 30° and 45° respectively, find the height of the tree. read less

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Answered on 11 Jan Learn Some Applications of Trigonometry

6. A tower subtends an angle at a point A in the place of its base and the angle of depression of the... read more
6. A tower subtends an angle α at a point A in the place of its base and the angle of depression of the foot of the tower at a point b ft. just above A is β. Prove that the height of the tower is b tan α cot β. read less

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Let CD is the height of the tower. ie, C is the bottom of the tower. Let AB is b ft. in trinagle ABC, (1) In triangle ACD, (2) From (1) and (2)/ therefore, read more

Let CD is the height of the tower. ie, C is the bottom of the tower.

Let AB is b ft. 

in trinagle ABC,

          (1)

In triangle ACD,

        (2)

From (1) and (2)/

therefore, 

 

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Answered on 12 Mar Learn Introduction to Trigonometry

9. In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.

Shailesh Kaushik

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Tan A = 1 means A is 45 degrees. which means cosA = cos45 = 1/√2 and sinA = sin45 = 1/√2 therefore, 2sinAcosA = 2 * 1/√2 * 1/√2 = 2 * (1/2) = 1 read more

Tan A = 1 means A is 45 degrees.

which means cosA = cos45 = 1/√2 and sinA = sin45 = 1/√2

therefore, 2sinAcosA = 2 * 1/√2 * 1/√2

                               = 2 * (1/2)

                               = 1

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Asked on 28/12/2021 Learn Some Applications of Trigonometry

5. A flagstaff stands at the top of a 5m high tower. From a point on the ground, the angle of elevation... read more
5. A flagstaff stands at the top of a 5m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flagstaff. read less

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Asked on 28/12/2021 Learn Some Applications of Trigonometry

7. A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From... read more
7. A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower. read less

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Asked on 28/12/2021 Learn Introduction to Trigonometry

5. Find the value of sin 45 °- Cos 45°.

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Asked on 28/12/2021 Learn Introduction to Trigonometry

6. If 4 tan θ = 3, evaluate (4 sin θ – cos θ + 1)/(4 sin θ + cos θ + 1).

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Asked on 28/12/2021 Learn Introduction to Trigonometry

7. Prove that [tan θ/(1 – cot θ)] + [cot θ/(1 – tan θ)] = 1 + sec θ cosec θ

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Asked on 28/12/2021 Learn Introduction to Trigonometry

8. Prove that: sin θ/(cot θ + cosec θ) = 2 + [sin θ/ (cot θ – cosec θ]

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