Trigonometry Grade 11

Question

A lighthouse operator spots two boats out in the ocean. One of the boats can be seen in the direction N35°W

and at an angle of depression of 4° and the other boat can be seen at S12°W and at an angle of depression of 6°.

If the lighthouse is 24 m tall, how far apart are the two boats?

Answer 1

Draw and label several diagrams.

First boat

Tower 24 m and angle of elevation 4°

Distance from tower tan 4° = 24 / d₁

Second boat

Tower 24 m and angle of elevation 6°

Distance from tower tan 6° = 24 / d₂

Angle between the two sightings is 133° (180° - 35° - 12°)

(Distance between boats)² = (d₁)² + (d₂)² - 2(d₁)(d₂) cos 133°