# Section 5.7: The Cosine Law

```Section 5.7: The Cosine Law

DO NOT get caught up in the letters! The side on the far left must correspond to the
angle on the far right.
For example, write the Cosine Law as it would apply to finding q in ∆.

Cosine Law is used when we know _______________________________________________

Or
__________________________________________________________________________________
Finding a side:
Given ΔABC with a = 5 cm, b = 7 cm and ∠C = 43°, find c.
Finding an angle: In ∆ , determine ∠ to the nearest degree if  = 55 ,
= 26 ,   = 32
EXAMPLE:
Determine each unknown to the nearest tenth.
EXAMPLE: A clock has a 30 cm long minute hand and a 21 cm long hour hand. How
far apart are the tips of the hands at 4 o’clock?
EXAMPLE: Mitchell wants his 8.0 m wide house to be heated with a solar hot – water
system. The tubes form an array that is 5.1 m long. In order for the system to be effective,
the array must be installed on the south side of the roof and the roof needs to be inclined
by 60°. If the north side of the roof is inclined more than 40°, the roof will be too steep for
Mitchell to install the system himself. Will Mitchell be able to do it?
EXAMPLE: The radar screen for an air traffic control tower shows a Piper Cherokee 15 km
from the tower in a direction 30° east of north, and a Cessna Skyhawk 16 kn from the tower
in a direction 40° east of north, at their closest approach to each other. If the two aircraft
are less than 2 km apart, the controller must file a report.
```