Download Cosine Law

Math 20-2
Trigonometry Lesson #3
The Cosine Law
Objective: By the end of this lesson, you should be able to:
- solve problems that require the use of the Cosine Law.
- draw a diagram to represent a problem that involves triangles.
Recall: To use the Sine Law, you must know an angle and the opposite side, as well as one
other side or angle.
But what if you aren’t given an opposite side-angle pair, as in the ABC shown below?
B
12.5 cm
25°
C
A
18.1 cm
For triangles where you are given either:

_____ sides and the angle _______________ them, or

____________ sides but _______ angles
there is another formula you can use, called the Cosine Law.
The Cosine Law
In any triangle ABC :
B
a
c
A
C
b
Note: c does not have to be the longest side of the triangle. It is simply the side ___________
the angle you are given. In fact, the Cosine Law can also be written in the forms:
Math 20-2
Trigonometry Lesson #3
e.g. 1) Find the length of side c in ABC , to the nearest tenth.
B
12.5 cm
25°
A
18.1 cm
C
The Cosine Law can also be used to find an angle when all three sides are given. In this case, we
can rearrange the Cosine Law as follows:
* Make sure that you substitute in the side lengths so that the c 2 value is the one
____________________ the angle you are trying to find.
e.g. 2) The Lions’ Gate Bridge in Vancouver is supported by triangular braces with side lengths
14 m, 19 m, and 12.2 m. Determine the measure of the angle opposite the 14-m side, to
the nearest degree.
Math 20-2
Trigonometry Lesson #3
Sometimes a problem involving an oblique triangle involves two steps to solve.
e.g. 3) The leaning tower of Pisa is 56 m tall and leans at an angle of 4° from the vertical. If you
stood 75 m from the tower, what would be the angle of elevation from that point to the
top of the tower?
Assignment:
p. 151-153 #4-5, 8-9, 13