Angles of Elevation and Depression - SS2 Mathematics Lesson Note

Simplifying and abstracting real-life problems makes finding their solutions easier. Such is the case with angles of elevation and depression.

Example: A man \(1.5m\) tall is \(10m\) from the foot of a vertical tower. He observes that the angle of elevation to the top of the tower is \(45{^\circ}\). Find the height of the tower.

Solution

\[Height\ of\ the\ tower = height\ of\ the\ tower\ from\ eye\ level\ to\ the\ top + height\ of\ the\ tower\ from\ eye\ level\ to\ the\ bottom\]

\[height\ of\ the\ tower\ from\ eye\ level\ to\ the\ bottom = 1.5m\]

\[height\ of\ the\ tower\ from\ eye\ level\ to\ the\ top:\]

\[\tan{45{^\circ}} = \frac{h}{10}\]

\[h = \tan{45{^\circ} \times 10}\]

\[h = 10m\]

\[Height\ of\ the\ tower = 10m + 1.5m = \ 11.5m\]