Download Sine and Cosine Rule Applications File

Using the Sine and Cosine Rules
Non Right-Angled Triangle Trigonometry
By the end of this lesson you will be able to explain/calculate the
following:
1. Application of the Sine Rule
2. Application of the Cosine Rule
• If we are given a problem involving a triangle,
we must first decide which rule to use
• If the triangle is right angled then the
trigonometric ratios or Pythagoras’ Theorem can
be used
• For some problems we can add an extra line or
two to the diagram to create a right angled
triangle
• Use the cosine rule when given:
▫ three sides
▫ two sides and an included angle.
• Use the sine rule when given:
▫ one side and two angles
▫ two sides and a non-included angle
 but beware of the ambiguous case which can occur
when the smaller of the two given sides is opposite
the given angle.
A boat begins a journey on a bearing of N 6317' E and travels for 20 km.
1. How far east of its starting point is it?
It then changes to a bearing of S 734' E and travels for a further 35 km.
2. Through what angle did the boat turn?
3. How far is it now from its starting point?
4. What is the bearing of its end point from the starting point?
A boat begins a journey on a bearing of N 6317' E and travels for 20 km.
1. How far east of its starting point is it?
It then changes to a bearing of S 734' E and travels for a further 35 km.
2. Through what angle did the boat turn?
3. How far is it now from its starting point?
4. What is the bearing of its end point from the starting point?
y 2  20 2  352  2  20  35  cos 7051
 400  1225  1400 cos 7051
 1165.7406
y  34.143km
20 2  34.1432  352
cos A 
2  20  34.143
 0.2435
A  cos 1 (0.2435)
bearing  6317  7533
 7533
 13850