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Right Triangles

Angles in Standard Position

Sine Law & Ambiguous Case

Cosine Law

Problem Solving

Summary&Test

 

jdsmathnotes

 

 


 UNIT 6 : BASIC TRIGONOMETRY WITH TRIANGLES

 LESSON 1: SOLVING RIGHT TRIANGLES

 

 

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].

 

 

Text Box: Formula:
    c2 = a2 + b2

c = hypotenuse
a, b = other two sides
 

 

 

 

 

 

 

 

 

 

 

 

 


Primary Trigonometric Ratios :

Text Box:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

Example 1:

Find the six trigonometric ratios for < P in fraction form and in decimal form (nearest hundredth).

 

 

 

Solution:

First calculate the hypotenuse using the Pythagorean Theorem.

 


 

 


 

 

 

Example 2: Right Triangles finding a side

CASE 1: Given a right triangle with one side and one angle known.

Find side x in the right triangle below.

 

Solution:

x = side opposite and 14.4 = side adjacent relative to 42o. Hence we use the tangent ratio since it involves opposite and adjacent.

 

 

 

 

Example 3: Right Triangles finding an angle

CASE 2: Given a right triangle with two sides known.

Find < A in the right triangle below.

 

Solution:

 

15.9 = hypotenuse and 12.3 = side adjacent relative to <A. Hence we use

the cosine ratio since it involves hypotenuse and adjacent.

 

 

 

Text Box: Note: As the above 2 examples show, a right triangle can be solved if you are given either 2 sides, in which case you can find one of the acute angles OR if you are given 1 side and 1 angle, in which case you can find another side.
 

 

 

 

 


 

Text Box: Note:  Triangle convention for naming sides and angles.
	a is the side opposite < A                                                                               
	b is the side opposite < B                                                                                   
	c is the side opposite < C

 

 

 

 

 

 

 

 

 

 

 

 

Example 4: Solving Right Triangles Finding all unknown sides and angles.

 

 

Solution: Find side a first.

a = side opposite and 8.4 = side adjacent relative to 38o. Hence we use the tangent ratio since it involves opposite and adjacent.

 

 

To find c, we could use either trigonometry as above or Pythagoras.

 

 

 

Example 5: Right Triangles Two Triangle Questions.

 

Find DG to the nearest tenth in the diagram below.

 

 

Solution:

We must use the triangle with 3 elements known. Hence we first find side DF in this triangle.

 

 

 

 

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