applications of trigonometry - A tower stands vertically on the ground. From a point which is 15 meter away from the foot of the tower, the angle of elevation of the top of the tower is 45º. What is the height of the tower?

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Analyse the given data.

Key words to understand the question.

A line joining the eye of the observer and object viewed by the observer. This line is called “line of sight”.

The line of sight is above the horizontal line and angle between the line of sight and the horizontal line is called angle of elevation.

The line of sight is below the horizontal line and angle between the line of sight and the horizontal line is called angle of depression.

Step 2: When we want to solve the problems of heights and distances, we should consider the following:

All the objects such as towers, trees, buildings, ships, mountains etc. shall be considered as linear for mathematical convenience.

The angle of elevation or angle of depression is considered with reference to the horizontal line.

Step 3: According to the given data make a imaginary figure.

GIVEN: Angle of elevation = 45\degree

Distance between the foot of the tower and the observation point = 15 meters

Height of the tower = ?

AB - tower height

Step 4: Find the suitable trigonometric ratio to calculate the height of the tower

NOTE: We know the adjacent side and we need to find the opposite side.

Hence we need to consider the trigonometric ratio “tan” .

\tan \theta = \frac{opposite}{adjacent}

\tan45\degree=\frac{opposite}{15}

Opposite side = 15 meters

Height of the tower = 15 meters