Home Right Triangles Angles in Standard Position Sine Law & Ambiguous Case Cosine Law Problem Solving Summary&Test

UNIT 6  : BASIC TRIGONOMETRY WITH TRIANGLES

LESSON 5:  PROBLEM SOLVING

Right Triangles Problems:

Example 1:

John is standing 12 m from the base of a cedar tree in his backyard.  The angle of elevation of the top of the tree is 480.  calculate the height of the tree.

Solution: The angle between the horizontal and the line of sight (AB) of the top of the tree is the ANGLE OF ELEVATION ( <ABC in diagram)

 A                                             h          B                               C                                       12 m    Angle of elevation = 480

Example 2:

From the top of a cliff 15 m high, the angle of depression of a sailboat on the lake is 350.  Find the distance of the boat from the cliff.

Solution: The angle between the horizontal (dashed line AD) and the line of sight (AC) of the boat is the ANGLE OF DEPRESSION ( <DAC in diagram)

A                                                        D

)Angle of depression = 350

15 m

B                  x                     C

Oblique Triangle Problems.

Example 3:

Find the distance up the slope DE of the mountain if the angles of elevation of the peak from directly opposite sides of the mountain are 480 and 540.  The distance EF is 900 m.

D

f

480                                       540

E                            900 m                                F

Solution:

First find the measure of  < D:    180o – (48o + 54o) = 78o

Now find f using the sine law. This is the AAS case.

Example 4:

Paul travels due east at 90 km/h for 3 hours.  George travels N300E at 110 km/h for 2 ½ hours.  How far apart are they if they started from the same location?

Solution:

Paul travels a distance of 90 x 3 = 270 km. due east.  George travels 110 x 2.5 = 275 km at an angle of 600 to Paul’s path.

N                        G

275

300

E

S                       270                              P

This is the SAS case.  Use the cosine law for side GP.