HOMEWORKDraw separate triangles for (a),

(b) and (c)

Bearings

Example State the following bearings.

060° 322° 202°

30°

N

E

S

W

38°

N

E

S

W 68°

N

E

S

W52°60°

22°

A bearing is the direction of a point from a starting point.

A bearing is measured from North in a clockwise direction.True bearings always have three figures.

BearingsExampleBob walks on a bearing of 123°. He finishes up 130m south (but not exactly south) of his starting position. How far did he walk?

123°

N

130m

57°

d

Swap the d and cos57°.

d = 23869mHe walked 239m (3 s.f.)

He starts here130m

A H

Soh Cah Toa

57°

Steps1. Draw diagram2. Label sides3. Identify trig ratio.4. Form an equation5. Solve the equation6. Answer the question

Angle of elevationWhen looking up towards an object, the angle of elevation is defined as the angle between the line of sight and the horizontal.

θ angle of elevationhorizontal

line of sight

Example1) The angle of elevation of a radio mast from a point 27m from the base is 59°. What is the height of the mast?

Steps1. Draw diagram2. Label sides3. Identify trig ratio.4. Form an equation5. Solve the equation6. Answer the question

59°27m

h

Angle of depressionWhen looking down towards an object, the angle of depression is defined as the angle between the line of sight and the horizontal.

θ angle of depressionhorizontal

line of sight

Example2) The angle of depression of a boat at sea from the top of a cliff 13m high is 23°46’. How far is the boat from the top of the cliff?

Steps1. Draw diagram2. Label sides3. Identify trig ratio.4. Form an equation5. Solve the equation6. Answer the question

23°46’

13md

angle of θ depression

the angle of elevation and depression diagrams can be drawn in similar ways.

sin23°46’ = 13/d

d = 13/sin23°46’

Swap the d and sin23°46’.

d = 2326mthe boat is 2326m from the top of the cliff.

Ex M 18.3Page 532

Q 1 – 3Then choose from

Q6 onwards

12 minutes