A person is standing 20 m from the base of a phone tower.

The angle of elevation of the top of the tower is 60 degrees.

Find the height of the tower, giving your answer to one decimal place.

The angle of depression from an observer from the top of a cliff to a row boat is 6 degrees.

The cliff is 25 m above sea level.

The horizontal distance from the boat to the cliff is?

The angle of elevation from a marker on the ground to the top of a building 100 m high is 22\(^\circ \).

Find the distance the marker must be moved so that the angle of elevation is 40\(^\circ \).

An observer notices a plane flying directly overhead.

Two minutes later, the plane is at an angle of elevation of 27 degrees.

The plane is travelling at a constant speed.

After a further 2 minutes, the angle of elevations is?

Find the angle of elevation of the sun when the length of the shadow of a pole is \(\sqrt 3 \) times the height of the pole.

From the top of a 200 m tower, the angle of depression of a car is \(48^\circ \).

How far is the car from the foot of the tower?

Answer to the nearest metre.

A ladder with its foot on a horizontal flat surface rests against a wall.

It makes an angle of \(60^\circ \) with the horizontal.

The foot of the ladder is 50 m from the base of the wall.

Find the height of the point where the ladder touches the wall, correct to 1 decimal place.

A hot air balloon is 250 m above Emily.

Emily is 500 m away from Sophia.

What is the angle of depression of the balloon to Sophia, correct to nearest degree.

From the top of a spire, 50 m tall, 2 cars are observed.

One is directly east of the tower and one is directly west.

The eastern car has an angle of depression of \(50^\circ \) and the car on the west has an angle of depression of \(35^\circ \).

How far are the 2 cars apart? 

A man on the deck of a ship is \(12~\text{m}\) above water level.

He observes that the angle of elevation of the top of a cliff is \(54 ^{\circ}\) and the angle of depression of the base is \(25^{\circ}\).

Find:

a) the distance of the cliff from the ship, correct to 2 decimal places.

b) the height of the cliff if the base of the cliff is at sea level, correct to 2 decimal places.

The angle of elevation from a point on level ground (C) to the top of the building (AB) is \(25^\circ \). Given that the height of the building is 120 m, find the distance (CD), the point must be moved so that the angle of elevation is \(40^\circ \). 

The angle of depression from an observer from the top of a cliff to a boat is \({4^o}\). The cliff is 40 m above sea level. The horizontal distance from the boat to the cliff is?

The angle of elevation from a point on level ground to the top of a tree is \({20^\circ}\). From a point 10 m closer to the base of the tree the angle of elevation is \({45^\circ}\) to the top of the tree. How high is the tree?

A section of a rollercoaster ride has a \(64^\circ \) angle of depression. If the length of the section is 48 m, what is the length of its vertical drop, correct to one decimal place?

Bugs Bunny was 66 m below ground, digging his way toward Pismo Beach, when he realized he wanted to be above ground. He turned and dug through the dirt diagonally for 160 meters until he was above ground.

What is the angle of elevation, to the nearest degree, of Bugs Bunny’s climb?

Joseph finds that the angle of elevation of a cliff, 520 m above sea level, is \(44^\circ \). After walking towards the cliff, he finds that the angle of elevation increases to \(60^\circ \). How far did Joseph walk?

A radio station tower was built in two sections. From a point 78 feet from the base of the tower, the angle of elevation of the top of the first section is \(35^\circ \) and the angle of elevation of the top of the second section is \(60^\circ \). To the nearest foot, what is the height of the top section of the tower?

A point, \(P\), lies between a flagpole, 20 metres high, and a tower, 32 metres tall. Candida is standing between the flagpole and the tower. From Candida’s position, the angle of elevation to the top of the flagpole is \(34^\circ \) and to the top of the tower is \(73^\circ \).

Calculate the direct distance between the base of the flagpole and the bottom of the tower nearest to two decimal places.

A hilltop is viewed from two different locations. The walking trail up the mountain is 450 m long at an angle of elevation of \(12^\circ \). The bus travels on a road that is 1.1 km long on the opposite side of the mountain.

Calculate the angle of elevation of the road to one decimal place.