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

UNIT 6  : BASIC TRIGONOMETRY WITH TRIANGLES

LESSON 6:  UNIT SUMMARY

Pythagorean Theorem:

In any right triangle, the square on the hypotenuse [c] equals the sum of the squares on the other two sides [a,b].

a          c

b

Primary Trigonometric Ratios :

Example : Right Triangles – Two Triangle Questions.

Find DG to the nearest tenth in the diagram below.

D

54.2o                                               31.6o

E                                                      G

9.7 cm    F

Angles in Standard Position:

Definition:   An angle is in standard position if it has its vertex at the origin and  initial arm along the positive x-axis.  The terminal arm is found by rotating the initial arm about the origin to a terminal position in one of the 4 quadrants.  The rotation is positive if it is in the counter – clockwise direction and negative if in the clockwise direction.

Example :

Solution:

 x = 4 y = 3 r = 5

Example : Angles greater than 900

Solution:

 x = -5 y = 12 r = 13

Note that sine is positive and cosine and tangent are negative for a second quadrant angle.

Result:  To find the trigonometric ratios of angles between 90o and 180o, use the following rules:

The Sine Law:

The sine law is used to solve oblique triangles, that is triangles which are not right angled.

A

c                                             b

B                             a                                           C

C

9.6                h            9.6           12.4

A1                                                                          420      B

A2

The Cosine Law:

The cosine law is  also used to solve oblique triangles, that is triangles which are not right angled.

It is used in the following two situations.

1.  Given two sides and a contained angle (SAS),  use one of the following 3 formulas to find the third side.

2.  Given  three sides  (SSS), use one of the following 3 formulas to find an angle.