## HEIGHT AND DISTANCE TRICKS

• **Line of sight** is a straight line from our eye to the object.

•

**:If an object is below the horizontal line from the eye, we have to lower our head to view the object. In this process our eyes moves through an angle. This angle is called the angle of depression. The angle of depression of an object viewed is the angle formed by the line of sight with the horizontal line, when the object is below the horizontal line.***Angle of depression*•* Angle of elevation*:If an object is above the horizontal line from our eyes we have to raise our head to view the object. In this process our eyes move through an angle formed by the line of sight and horizontal line which is called the angle of elevation.

**Few things to remember before we start solving problems :**

• Read the statements of the question carefully.

• Construct a diagram for the problem for better understanding and visualization of the problem.

• Identify the trigonometrical ratio that will be useful for solving the problem.

• Real world problems will not have standard angles always. So use the below table whenever and wherever necessary.

#### Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

Correct!
Wrong!

#### The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

Correct!
Wrong!

#### From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

Correct!
Wrong!

#### The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:

Correct!
Wrong!

#### An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is:

Correct!
Wrong!

Heights and Distances

Marvellous... You are quite good at estimating heights and distances

Great....You can calculate distances easily

Need to work hard.... Try to estimate things in real world

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