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IB Mathematics: Applications and Interpretation HL · 12.10: Geometry & Trigonometry · 12.10.7

Name Date

Angles of elevation and depression Problem set A

Draw a diagram first and mark the horizontal. Give answers to 3 significant figures.

Difficulty: first skills applying them stretch

Skills

  1. A lamp post is seen from a point 18 m from its foot. The angle of elevation of the top of the lamp post is 32°, and the observer's eyes are 1.7 m above the ground. Find the height of the lamp post.

    18 mh32°AT

  2. From the top of a cliff 45 m above the sea, the angle of depression of a boat is 23°. Find the horizontal distance of the boat from the foot of the cliff.

    45 md23°BCT

  3. From a point A the angle of elevation of the top of a flagpole is 42°. From a point 25 m further from the flagpole, on the same level and in line with it, the angle of elevation is 27°. The observer's eyes are 1.5 m above the ground. Find the height of the flagpole.

    25 mh27°42°BAT

In context

  1. The angle of elevation of the top of a church spire from a point A is 31°. Anil walks 60 m directly away from the spire to a point B, where the angle of elevation is 19°. His eyes are 1.7 m above the ground. Find the height of the spire.

    60 mh19°31°BAT

  2. From the top of a cliff the angle of depression of a boat is 15°. The boat sails 200 m directly towards the cliff and the angle of depression is then 28°. Find the height of the top of the cliff above the sea.

    200 mh15°28°BAT

Stretch

  1. The top of a flagpole is 12 m above an observer's eye level. The angle of elevation of the top is 40° from one point. The observer walks directly away from the flagpole, and the angle of elevation of the top is then 25°. How far does the observer walk?

jmaths.xyz · AI HL · 12.10.7 Angles of elevation and depression