Angles of Elevation and Depression - SS2 Mathematics Lesson Note

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

Example: A man $1.5 m$ tall is $10 m$ 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

$H e i g h t o f t h e t o w e r = h e i g h t o f t h e t o w e r f r o m e y e l e v e l t o t h e t o p + h e i g h t o f t h e t o w e r f r o m e y e l e v e l t o t h e b o t t o m$

$h e i g h t o f t h e t o w e r f r o m e y e l e v e l t o t h e b o t t o m = 1.5 m$

$h e i g h t o f t h e t o w e r f r o m e y e l e v e l t o t h e t o p :$

$\tan 45^{\circ} = \frac{h}{10}$

$h = \tan 45^{\circ} \times 10$

$h = 10 m$

$H e i g h t o f t h e t o w e r = 10 m + 1.5 m = 11.5 m$