Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) What is meant by the "angle of depression"?

The angle of depression is the angle between the horizontalverticaldiagonal line and the line of sight when looking downwardupwardsideways.

Perfect! It's always measured downward from the horizontal.

(2) Define "line of sight" in a right-angled triangle.

The line of sight is the straight linecurved linebroken line joining the observer's eyeobserver's feetobject to the object being viewedgroundhorizon.

Excellent! It's the direct visual connection between observer and object.

(3) If a man sees the top of a pole at an angle of elevation of 30°, what trigonometric ratio would you use to find the height of the pole?

The trigonometric ratio to use is tansincossec 30°, because tan θ = oppositeadjacentadjacentoppositeoppositehypotenuse.

Correct! tan θ = heightdistance for angle of elevation problems.

(4) Write the formula to find the height of an object when distance and angle of elevation are known.

Height = Distance × tan θsin θcos θcot θ

Perfect! This comes from tan θ = heightdistance.

(5) What is the angle of elevation of the top of a pole when its height and shadow are equal?

When height = shadow, tan θ = heightshadow = , so θ = °

Excellent! When tan θ = 1, the angle is 45°.

Short Answer Questions (2 Marks Each)

(1) The angle of elevation of the top of a tower from a point on the ground is 60°. If the height of the tower is 253 m, find the distance of the point from the foot of the tower.

Using the values given, we get distance = m

Perfect! The distance is 25 meters from the tower.

(2) A balloon is flying at a height of 50 m. The angle of elevation of the balloon from a point on the ground is 30°. Find the distance of the balloon from the point on the ground.

Distance from point on ground to balloon = m

Excellent! The balloon is 100 m away from the observer.

(3) A man 1.8 m tall observes the top of a tower at an angle of elevation of 45°. The distance between the man and the tower is 28.2 m. Find the height of the tower.

Height of tower = m

Perfect! The tower is 30 meters tall.

(4) From a point on the ground, the angle of elevation of the top of a flag pole is 60°. If the height of the pole is 17.3 m, find the distance from the point to the base of the pole.

Distance from the point to the base of the pole = m (Round off to nearest whole number)

Excellent! The distance is approximately 10 meters.

(5) A building and a tower stand on a level ground. From the top of the building, the angle of elevation of the top of the tower is 30° and the angle of depression of the foot of the tower is 60°. If the height of the building is 20 m, find the height of the tower.

Height of the tower = m (fraction form) ≈ m (Round off to two decimal places)

Excellent problem-solving! The tower height is 803 meters.

(6) An observer at a height of 40 m observes the top of a tower at an angle of depression of 45°. Find the distance between the observer and the top of the tower.

Distance from observer to top = 402202 m ≈ meters (Round off to two decimal places)

Perfect! The distance is 402 ≈ 56.57 meters.

Long Answer Questions (4 Marks Each)

(1) From the top of a tower 50 m high, the angle of depression of a car on the road is 30°. Find how far the car is from the foot of the tower.

Horizontal distance between car and foot of tower = 503502 m ≈ m (Round off to one decimal place)

Excellent! The car is 503 meters from the tower.

(2) Two poles of equal height are standing opposite each other on either side of a road. The angle of elevation of the top of the poles from a point between them on the road is 60° and 30° respectively. Find the distance between the poles if the point is 20 m from the foot of the shorter angle pole.

Total distance between poles = m (fraction form) ≈ m (Round off to two decimal places)

Perfect! The distance between poles is 803 meters.

(3) A man standing on top of a 60 m high building observes the angle of depression of a car on the ground to be 30°. Find the distance of the car from the building.

Distance between car and building = 6031203 m ≈ m (Round off to one decimal place)

Excellent! The car is 603 meters from the building.

(4) A man standing on a platform finds that the angle of elevation of the top of a tower is 60° and the angle of depression of the foot of the tower is 30°. If the height of the platform is 2 m, find the height of the tower.

Total height of tower = m

Perfect! The tower is 8 meters tall.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) If the angle of elevation is 60° and the height of the object is known, the base is given by:

(a) h × tan 60° (b) h × sin 60° (c) h ÷ tan 60° (d) h × cos 60°

Correct! Since tan 60° = hbase, then base = h ÷ tan 60°.

(2) In a right triangle, if the opposite = 10 m and angle = 30°, then hypotenuse =

(a) 103 (b) 20 (c) 203 (d) 203

Correct! sin 30° = 10hypotenuse, so hypotenuse = 1012 = 20.

(3) A person standing on the ground sees the top of a tower at 60° and its foot at 30°, then the person is:

(a) At the base of the tower (b) At height equal to tower (c) Above ground level (d) None of these

Correct! Seeing both top and foot at different angles means the observer is elevated.

(4) If the angle of depression is 45° and the observer is 20 m high, the horizontal distance is:

(a) 10 m (b) 20 m (c) 30 m (d) 40 m

Correct! tan 45° = 20distance, so distance = 201 = 20 m.

(5) An object subtends angles of elevation 60° and 30° from two different points 50 m apart. The height of the object is:

(a) 43.3 m (b) 50 m (c) 86.6 m (d) 100 m

Correct! Using the two-point elevation formula: h = 5033 ≈ 43.3 m.

(6) If tan θ = 3, then the angle θ is:

(a) 30° (b) 45° (c) 60° (d) 90°

Correct! tan 60° = 3.

(7) Which of the following is true for a right triangle with angle of elevation 45°?

(a) Base = height (b) Base > height (c) Base < height (d) None

Correct! tan 45° = 1, so heightbase = 1, therefore base = height.

(8) The angle of depression is always measured:

(a) Vertically upward (b) Horizontally downward (c) From horizontal downward (d) Vertically downward

Correct! Angle of depression is measured downward from the horizontal line.

(9) If height = 10 m and angle of elevation is 60°, then base =

(a) 103 (b) 103 (c) 5 (d) 10

Correct! tan 60° = 10base, so base = 103.

(10) If the angle of elevation of the top of a pole is 60° and the base distance is 5 m, then the height of the pole is:

(a) 53 m (b) 10 m (c) 5 m (d) 2.5 m

Correct! height = base × tan 60° = 5 × 3 = 53 m.

Applications of Trigonometry Challenge

Determine whether these statements are True or False:

Applications of Trigonometry Quiz