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Heights And Distances Trigonometry Worksheet With Answers - The Institute Of Mathematical Science Page 3

Theodolite is an instrument which is used in measuring the angle be-

tween an object and the eye of the observer. A theodolite consists of two

graduated wheels placed at right angles to each other and a telescope. The

wheels are used for the measurement of horizontal and vertical angles. The

angle to the desired point is measured by positioning the telescope towards

that point. The angle can be read on the telescopic scale.

Figure 4: Theodolite

Deﬁnitions :

Let us deﬁne a few terminologies so that we can understand and implement

the concept of Trigonometry to ﬁnd the heights and distances.

• 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.

• Similarly, 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.

Heights And Distances Trigonometry Worksheet With Answers - The Institute Of Mathematical Science Page 3