Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Define the term "angle of elevation." Angle of elevation is the angle between the line and the line of sight when an object is the observer's eye level

Perfect! Angle of elevation is always measured upward from horizontal.

(2) What is meant by "line of sight"? Line of sight is the line joining the observer's to the being observed

Excellent! This is the imaginary line from eye to object.

(3) If the angle of elevation of the sun is 45°, what is the height of a pole whose shadow is 5 m long? Height = m

Perfect! When angle is 45°, height equals shadow length.

(4) Name the trigonometric ratio used to relate height and base in a right triangle when angle and base are known.

Correct! Tangent ratio connects angle with height and base.

(5) What is the value of tan 45°? tan 45° =

Perfect! This is one of the standard angle values.

Short Answer Questions (2 Marks Each)

(1) From a point on the ground, the angle of elevation of the top of a pole is 30°, and the pole is 10 m tall. Find the distance from the point to the foot of the pole. distance = 10353 m

Excellent! Used tangent ratio correctly for height-distance problem.

(2) A ladder is leaning against a wall and makes an angle of 60° with the ground. If the foot of the ladder is 4 m from the wall, find the length of the ladder. length = m

Perfect! Used cosine ratio to find hypotenuse (ladder length).

(3) The angle of elevation of the top of a tower from a point on the ground is 45°. If the tower is 20 m tall, find the distance of the point from the base of the tower. distance = m

Excellent! When angle is 45°, distance equals height.

(4) A kite is flying at a height of 30 m. The string attached to it makes an angle of 60° with the ground. Find the length of the string (Assume the string is straight). Length = 203153 m

Perfect! Used sine ratio to find hypotenuse (string length).

(5) If the angle of elevation of the top of a tree is 30° and the distance from the observer to the tree is 10 m, find the height of the tree. h = 103103 m

Excellent! Applied tangent ratio systematically.

(6) A man observes the top of a lighthouse at an angle of elevation of 45°. If he is standing 40 m away from the base, what is the height of the lighthouse? h = m

Perfect! When angle is 45°, height equals horizontal distance.

Long Answer Questions (4 Marks Each)

(1) From a point 50 m away from the foot of a tower, the angle of elevation of the top is 60°. Find the height of the tower. h = 503303 m

Excellent! Systematic solution using trigonometric ratio.

(2) A man is standing on the ground, 30 m away from a building. He observes the top of the building at an angle of elevation of 45°. Find the height of the building. h = m

Perfect! Applied the special property of 45° angle.

(3) An observer from a lighthouse 75 m high observes a boat at an angle of depression of 30°. Find the distance of the boat from the foot of the lighthouse. d = 753503 m

Excellent! Used the relationship between angles of depression and elevation.

(4) The angle of elevation of the top of a tower from a point on the ground is 30°. If the height of the tower is 100 m, find the distance of the point from the base of the tower. d = 1003753 m

Perfect! Complete solution with proper steps and reasoning.

Part B: Objective Questions (1 Mark Each)

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

(1) The trigonometric ratio used when height and base are known is:

(a) sin θ (b) cos θ (c) tan θ (d) cot θ

Correct! tan θ = oppositeadjacent = heightbase in elevation problems.

(2) If the height of a tower is 10 m and the distance from the observer is also 10 m, the angle of elevation is:

(a) 30° (b) 45° (c) 60° (d) 90°

Correct! When height = base, tan θ = 1, so θ = 45°.

(3) The angle of elevation increases as the observer:

(a) Moves away (b) Moves closer (c) Moves up (d) Stays still

Correct! Moving closer makes the object appear higher, increasing the angle.

(4) If tan θ = 1, then the angle θ is:

(a) 30° (b) 60° (c) 45° (d) 90°

Correct! tan 45° = 1 is a standard trigonometric value.

(5) The angle between the line of sight and the horizontal when an object is above the observer is:

(a) Angle of depression (b) 180° (c) Right angle (d) Angle of elevation

Correct! Angle of elevation is measured upward from horizontal.

(6) In a right triangle, if the opposite side is 5 and adjacent side is 5, then tan θ =

(a) 0 (b) 1 (c) 2 (d) 5

Correct! tan θ = oppositeadjacent = 55 = 1.

(7) A boy is flying a kite at a height of 20 m. The thread makes an angle of 30° with the ground. The length of the thread is:

(a) 40 m (b) 203 m (c) 403 m (d) 403 m

Correct! Using sin 30° = 20length: 12 = 20length, so length = 40 m.

(8) The value of sin 30° is:

(a) 1 (b) 32 (c) 12 (d) 0

Correct! sin 30° = 12 is a standard trigonometric value.

(9) The angle of depression is measured:

(a) From vertical down (b) From vertical up (c) From horizontal down (d) From horizontal up

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

(10) If a person observes a tower at 60° and he is 10 m away from it, the height of the tower is:

(a) 103 m (b) 5 m (c) 20 m (d) 10 m

Correct! Using tan 60° = h10: 3 = h10, so h = 103 m.

Basic Trigonometry Applications Challenge

Determine whether these statements about trigonometry applications are True or False:

Basic Trigonometry Applications Quiz