Some Applications of Trigonometry quiz

The angle of elevation of the top of a tower from a point 20 m away from its foot is 45 degrees. The height of the tower is:

If the height of a pole and the length of its shadow are in the ratio sqrt(3) : 1, the angle of elevation of the Sun is:

The angle formed by the line of sight with the horizontal when the object is below the horizontal level of the eye is called the:

A ladder 10 m long makes an angle of 60 degrees with the ground. The height it reaches on the wall is:

From a point on the ground 10 sqrt(3) m from the foot of a tower, the angle of elevation of the top is 30 degrees. The height of the tower is:

As an observer moves away from a tower, the angle of elevation of the top of the tower:

The length of the shadow of a 6 m tall pole when the Sun's altitude is 30 degrees is:

A kite string 100 m long makes an angle of 30 degrees with the ground. The height of the kite is:

From the top of a 50 m high cliff, the angle of depression of a boat is 45 degrees. The distance of the boat from the foot of the cliff is:

If the angle of elevation of the Sun is 45 degrees, the length of the shadow of a 15 m tree is:

The angle of elevation of the top of a building from a point on the ground 50 m away is 60 degrees. Find the height of the building. (2 marks)

A ladder leaning against a wall makes an angle of 60 degrees with the ground. The foot of the ladder is 2.5 m away from the wall. Find the length of the ladder. (2 marks)

Find the angle of elevation of the Sun when the shadow of a 10 m pole is 10sqrt(3) m long. (2 marks)

From the top of a 60 m cliff, the angle of depression of a car on the road is 30 degrees. How far is the car from the foot of the cliff? (2 marks)

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45 degrees. Find the height of the chimney. (2 marks)

A wire is tied to the top of a 12 m vertical pole and fixed to the ground, making an angle of 30 degrees with the ground. Find the length of the wire. (2 marks)

From a point on a bridge 3 m above the water, the angle of depression of a point on one bank of the river is 45 degrees. How far is the bank from the point directly below the observer? (2 marks)

A vertical pole 6 m high casts a shadow 2sqrt(3) m long on the ground. Find the angle of elevation of the Sun. (2 marks)

Draw a rough figure to show the angle of elevation of the top of a tree from a point 15 m from its foot as 60 degrees, and find the height of the tree. (2 marks)

The string of a kite is 50 m long and makes an angle of 60 degrees with the horizontal. Find the height of the kite, assuming no slack. (2 marks)

From a point P on the ground, the angle of elevation of the top of a 10 m tall building is 30 degrees. A flag is hoisted at the top of the building, and the angle of elevation of the top of the flagstaff from P is 45 degrees. Find the length of the flagstaff and the distance of the building from P. (Use sqrt(3) = 1.732) (3 marks)

The angle of elevation of the top of a building from the foot of a tower is 30 degrees and the angle of elevation of the top of the tower from the foot of the building is 60 degrees. If the tower is 50 m high, find the height of the building. (3 marks)

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60 degrees and the angle of depression of its foot is 45 degrees. Determine the height of the tower. (3 marks)

As observed from the top of a 75 m high lighthouse above sea level, the angles of depression of two ships are 30 degrees and 45 degrees. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (3 marks)

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top is 60 degrees. From another point 20 m away from this point on the line joining it to the foot of the tower, the angle of elevation is 30 degrees. Find the height of the tower and the width of the canal. (3 marks)

Read the passage and answer the questions. A group of students visits a riverside. Standing on a bridge 3 m above the water, Arun observes that the angles of depression of the two banks, on opposite sides of the river, are 30 degrees and 45 degrees. (i) Draw a rough figure and find the distance of the nearer bank (angle 45 degrees) from the point directly below Arun. (ii) Find the distance of the farther bank (angle 30 degrees) from the same point. (iii) Find the width of the river. (Use sqrt(3) = 1.732) (5 marks)

Read the passage and answer the questions. An aeroplane flying at a constant height of 3600sqrt(3) m is observed from a point A on the ground. The angle of elevation is 60 degrees at first, and after a flight of 30 seconds it changes to 30 degrees. (i) Find the horizontal distance of the plane from A in the first position. (ii) Find the horizontal distance in the second position. (iii) Find the speed of the plane in km/h. (5 marks)

Read the passage and answer the questions. A fire in a building is seen by a fire officer standing on the ground 20 m away from the building. The angle of elevation of the window on fire is 60 degrees. The fire engine has a ladder that can be raised at an angle of 60 degrees from the same point. (i) Find the height of the window from the ground. (Use sqrt(3) = 1.732) (ii) Find the minimum length of the ladder needed to reach the window. (iii) If the ladder were placed at 45 degrees, how far from the building should its foot be? (5 marks)

Read the passage and answer the questions. A student measures the height of her school flagpole. Standing 15 m from the pole, she finds the angle of elevation of the top to be 45 degrees. Her eyes are 1.5 m above the ground. (i) Draw a figure and mark the right triangle used. (ii) Find the height of the top of the pole above her eye level. (iii) Find the total height of the flagpole. (5 marks)

Read the passage and answer the questions. A security guard is on a watchtower 20 m high in a park. He sees a child at an angle of depression of 30 degrees and a dog at an angle of depression of 60 degrees, both on the same side of the tower and in a straight line with its foot. (i) Find the distance of the child from the foot of the tower. (ii) Find the distance of the dog from the foot of the tower. (iii) Find the distance between the child and the dog. (Use sqrt(3) = 1.732) (5 marks)

The angles of elevation of the top of a tower from two points on the ground at distances of a m and b m from its base, in the same straight line, are 60 degrees and 30 degrees. Draw the figure and prove that the height of the tower is sqrt(ab) m. Hence find the height when a = 4 and b = 12. (6 marks)

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45 degrees and 60 degrees respectively. Draw the figure and find the height of the tower. (Use sqrt(3) = 1.732) (6 marks)

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from her eyes at an instant is 60 degrees. After some time, the angle of elevation reduces to 30 degrees. Draw the figure and find the distance travelled by the balloon during the interval. (6 marks)

From the top of a building 60 m high, the angles of depression of the top and the bottom of a vertical lamp post are observed to be 30 degrees and 60 degrees. Draw the figure and find (i) the horizontal distance between the building and the lamp post (ii) the height of the lamp post. (Use sqrt(3) = 1.732) (6 marks)

Explain the terms line of sight, angle of elevation and angle of depression with a single labelled diagram showing a person on a hill looking up at a bird and down at a boat. Then solve: a person on the hill 100 m high sees a boat at an angle of depression of 30 degrees; find the distance of the boat from the foot of the hill. (Use sqrt(3) = 1.732) (6 marks)