Some Applications of Trigonometry

Which statement best summarizes the chapter "Some Applications of Trigonometry"?

1. The chapter deals only with trigonometric identities.
2. The chapter explains how trigonometric ratios, along with angles of elevation and depression, are used to calculate heights and distances in practical situations such as surveying, navigation, architecture, engineering, and construction.
3. The chapter studies circles only.
4. The chapter has no practical use.

Which is the first step in solving a height-and-distance problem?

1. Memorize the answer
2. Draw a neat labelled diagram
3. Use the distance formula immediately
4. Find the midpoint

Which standard value is useful for solving many trigonometric application problems?

1. tan 45° = 1
2. tan 45° = 2
3. sin 45° = 1
4. cos 45° = 2

If the horizontal distance doubles while the angle of elevation remains the same, the height will:

1. Double
2. Become half
3. Remain unchanged
4. Become zero

Which ratio is used when the opposite side and hypotenuse are known?

1. Cos θ
2. Tan θ
3. Sin θ
4. Sec θ

Which profession commonly uses applications of trigonometry?

1. Surveyors
2. Architects
3. Engineers
4. All of the above

A ladder rests against a wall making an angle of 60 degrees with the ground. The ladder represents the:

1. Opposite side
2. Adjacent side
3. Hypotenuse
4. Height

Which trigonometric ratio relates the adjacent side and hypotenuse?

1. Sin θ
2. Cos θ
3. Tan θ
4. Cot θ

From the top of a building, the angle of depression of a car is 30 degrees. The angle of elevation of the building from the car is:

1. 60°
2. 45°
3. 30°
4. 90°

If the angle of elevation increases while the distance remains fixed, the height of the object will:

1. Decrease
2. Increase
3. Remain unchanged
4. Become zero

Which of the following is essential for solving application-based trigonometry problems?

1. Circle only
2. Right-angled triangle
3. Rectangle only
4. Square only

A person stands 20 m from the foot of a tower. If the angle of elevation is 45 degrees, what is the height of the tower?

1. 10 m
2. 20 m
3. 30 m
4. 40 m

Which trigonometric ratio is most commonly used when the height and horizontal distance are involved?

1. Sine
2. Cosine
3. Tangent
4. Secant

The angle formed by looking downward from a higher point is called:

1. Angle of Elevation
2. Angle of Depression
3. Straight Angle
4. Reflex Angle

The angle formed by looking upward at the top of an object is called:

1. Angle of Depression
2. Angle of Elevation
3. Right Angle
4. Acute Angle

A kite is flying at a height of 40 m and the string makes an angle of 45° with the ground. Find the length of the string.

1. 20 m
2. 40 m
3. 40√2 m
4. 80 m

From a point 20 m away from the base of a tower, the angle of elevation is 60°. Find the height of the tower.

1. 10 m
2. 10√3 m
3. 20√3 m
4. 30 m

A pole is 20 m high. The angle of elevation of its top from a point is 60°. Find the distance of the point from the base of the pole.

1. 10 m
2. 10√3 m
3. 20√3 m
4. 15 m

A tower and a building are 30 m apart. From the top of the tower, the angle of depression of the base of the building is 45°. Find the height of the tower.

1. 15 m
2. 30 m
3. 60 m
4. 45 m

From the top of a 50 m high tower, the angle of depression of a car is 30°. Find the distance of the car from the base of the tower.

1. 25 m
2. 50 m
3. 50√3 m
4. 100 m

A ladder touches wall at 8 m height making 30° angle. Length of ladder is:

1. 8 m
2. 16 m
3. 8√3 m
4. 10 m

If shadow equals height, angle of elevation is:

1. 30°
2. 45°
3. 60°
4. 90°

Angle of depression from top of tower to object is 30°. Horizontal distance is 20 m. Height is:

1. 10√3 m
2. 20√3 m
3. 10 m
4. 5 m

A person observes top of building at 60° from 10 m distance. Height is:

1. 10 m
2. 10√3 m
3. 5√3 m
4. 20 m

A tree is 15 m high. Find angle of elevation from a point 15 m away.

1. 30°
2. 45°
3. 60°
4. 90°

From a point on ground, angle of elevation of top of tower is 30°. If distance is 10 m, height is:

1. 5 m
2. 5√3 m
3. 10√3 m
4. 10 m

A kite is flying at a height of 30 m with string making 60° angle with ground. Find length of string.

1. 30 m
2. 20 m
3. 60 m
4. 60√3 m

A pole casts a shadow of 6 m when the sun's angle of elevation is 30°. Find the height of the pole.

1. 2√3 m
2. 3√3 m
3. 6√3 m
4. 4√3 m

A tower casts a shadow 20 m long when the angle of elevation of the sun is 45°. Find the height of the tower.

1. 10 m
2. 15 m
3. 20 m
4. 25 m

A ladder 10 m long leans against a wall and makes an angle of 60° with the ground. Find the height reached by the ladder.

1. 5 m
2. 5√3 m
3. 10√3 m
4. 8 m