## Height and Distance MCQ

What is the height of a right-angled triangle if the angle opposite the base is 30 degrees and the base is 10 metres long?

Options:

a) 5 meters

b) 10 meters

c) 15 meters

d) 20 meters

Answer: c) 15 meters

The angle of depression of an object on the ground is 60 degrees as viewed from the top of a 40-meter tower. How far away from the tower’s base is the object?

Options:

a) 20 meters

b) 40 meters

c) 60 meters

d) 80 meters

Answer: c) 60 meters

As viewed from the top of a 40-meter tower, the angle of depression of an object on the ground is 60 degrees. How far is the object from the base of the tower?

Options:

a) 25 meters

b) 50 meters

c) 75 meters

d) 100 meters

Answer: c) 75 meters

If a right-angled triangle has a base that is 6 metres long, and a hypotenuse that is 10 metres long what is the measurement, of the angle that is opposite the base?

Options:

a) 30 degrees

b) 45 degrees

c) 60 degrees

d) 90 degrees

Answer: b) 45 degrees

The shadow of a tree stretches 15 metres. A 2-meter-tall person standing near to the tree casts a 1-meter-long shadow. How tall is the tree?Options:

a) 7 meters

b) 10 meters

c) 15 meters

d) 20 meters

Answer: d) 20 meters

The angle of elevation of a tower’s top is measured from a location 30 metres from the tower’s base. What is the tower’s height?

Options:

a) 10 meters

b) 20 meters

c) 30 meters

d) 40 meters

Answer: c) 30 meters

The base and hypotenuse of a right-angled triangle have lengths of 8 metres and 10 metres, respectively. What is the height’s length?

Options:

a) 6 meters

b) 7 meters

c) 8 meters

d) 9 meters

Answer: b) 7 meters

A car parked on the ground is 45 degrees lower than the top of a structure. If a structure is 20 metres tall, how far is the car from the base?

Options:

a) 20 meters

b) 30 meters

c) 40 meters

d) 50 meters

Answer: c) 40 meters

The opposing angle of a right-angled triangle is 60 degrees, and the base’s length is 12 metres. What is the hypotenuse’s length?

Options:

a) 6 meters

b) 12 meters

c) 24 meters

d) 36 meters

Answer: c) 24 meters

When viewed from a place 20 metres from the bas e of a tower , the top is elevated at a 30 degree angle. What is the height of the tower?

a) 10 meters

b) 20 meters

c) 30 meters

d) 40 meters

Answer: a) 10 meters

The wall is lined with a ladder. The ladder’s base is six metres from the wall, and it forms a 60-degree angle with the ground. What is the ladder’s length?

a) 3 meters

b) 6 meters

c) 12 meters

d) 36 meters

Answer: c) 12 meters

The wall has a ladder attached to it . The base of the ladder is six metres f,rom the wall and is at a 60-degree ,angle with the ground. How far up the ladder is it?

a) 25 meters

b) 50 meters

c) 100 meters

d) 150 meters

Answer: c) 100 meters

A flagpole is positioned on the ground vertically. The angle of elevation to the summit of the flagpole from a point 20 metres from its base is 45 degrees. What is the flagpole’s height?

a) 10 meters

b) 20 meters

c) 30 meters

d) 40 meters

Answer: a) 10 meters

A person is standing at the cliff’s edge and gazing down to a 45-degree depression. How far away from the person is the base of the cliff if they are 50 metres above it?

a) 35.36 meters

b) 50 meters

c) 70.71 meters

d) 100 meters

Answer: c) 70.71 meters

When the sun is at a 60-degree angle of elevation, a tree throws a shadow that is 8 metres long. What is the tree’s height?

a) 4 meters

b) 8 meters

c) 16 meters

d) 24 meters

Answer: d) 24 meters

There is a 20-meter ladder leaning up against a wall. The wall is 9 metres away from the ladder’s base. What angle does the ladder make with the ground?

a) 27.7 degrees

b) 36.9 degrees

c) 45 degrees

d) 60 degrees

Answer: b) 36.9 degrees

The angle of depression to a point on the ground from a building’ s top is 30 degrees. How far is the point on the ground , from the base of the building ,if it is 40 metres tall?

a) 20 meters

b) 40 meters

c) 69.3 meters

d) 80 meters

Answer: c) 69.3 meters

On a hill is a person standing. A tree at the bottom of the hill is 15 degrees higher than the ground. After walking 100 metres uphill, the person discovers that the tree’s elevation angle has changed to 30 degrees. What is the tree’s height?

a) 100 meters

b) 173.2 meters

c) 200 meters

d) 346.4 meters

Answer: b) 173.2 meters

A 10-meter pole casts a shadow that is 15 metres long. At the same time, an adjacent building’s shadow extends 30 metres in length. What is the building’s height?

a) 15 meters

b) 20 meters

c) 25 meters

d) 30 meters

Answer: c) 25 meters

A person standing 100 metres away is observing a tower’s top. The elevation angle is 30 degrees. The angle of elevation changes to 45 degrees if the person moves in close proximity by 50 metres. What is the tower’s height?

a) 50 meters

b) 75 meters

c) 100 meters

d) 150 meters

Answer: b) 75 meters

At an altitude of 80 metres above the ground , a kite is in the air. The kite’s string is at a 60-degree angle with the ground. How much string is there?

a) 80 meters

b) 120 meters

c) 160 meters

d) 200 meters

Answer: c) 160 meters

The angle of depression to a boat on the water from the top of a lighthouse is 45 degrees. How far is the boat from the lighthouse if the lighthouse is 50 metres high?

a) 50 meters

b) 70.71 meters

c) 100 meters

d) 141.42 meters

Answer: d) 141.42 meters

The height of a tower’s top is 60 degrees higher than a point ,on the ground,. The angle of elevation increases to 75 degrees if the individual moves in close proximity ,to the tower by 20 metres. What is the tower’s height?

a) 10 meters

b) 20 meters

c) 40 meters

d) 60 meters

Answer: c) 40 meters

A figure is perched atop a hill and is gazing below at a 30 degree depression. How far away from the person is the base of the hill if they are 100 metres above it?

a) 100 meters

b) 115.47 meters

c) 173.21 meters

d) 200 meters

Answer: b) 115.47 meters

When a pole is broken, the top portion hits the surface and forms a 30-degree angle with it. Eight metres separate the pole’s breaking point from the base. What is the pole’s height?

a) 4 meters

b) 8 meters

c) 16 meters

d) 24 meters

Answer: c) 16 meters