Sine rule: finding an angle
The Maths Habit
Give each side to 1 decimal place.
Angle A is 48°, angle B is 71° and side a is 9 cm. Find side b.
11.5 cmAngle A is 110°, angle B is 25° and side a is 15 cm. Find side b.
6.7 cmAngle A is 36°, angle B is 62° and side c is 12 cm. Find side a.
7.1 cm
Sam says the biggest angle in a triangle is always opposite the longest side. Is Sam right? Try to draw a triangle where he is wrong.
Sam is right: the bigger the angle, the longer the side opposite it
Which rule?
Two sides and an angle opposite one of them
Sine rule
A side of 6 cm is opposite angle x. A side of 9 cm is opposite an angle of 75°. Find x.
each angle over the side opposite itsin x6=sin 75°9
multiply both sides by 6sin x =0.6440
x =40.1°
A side of 5 cm is opposite angle x. A side of 7 cm is opposite an angle of 60°. Find x.
each angle over the side opposite itsin x5=sin 60°7
multiply both sides by 5sin x =0.6186
x =38.2°
A side of 6 cm is opposite angle x. A side of 9 cm is opposite an angle of 75°. Find x.
each angle over the side opposite itsin x6=sin 75°9
multiply both sides by 6sin x =0.6440
x =40.1°
A side of 8 cm is opposite angle x. A side of 11 cm is opposite an angle of 55°. Find x.
each angle over the side opposite itsin x8=sin 55°11
multiply both sides by 8sin x =0.5957
x =36.6°
A side of 10 cm is opposite an angle of 80°. A side of 7 cm is opposite angle x. Find x, then the third angle.
43.6° and 56.4°Why can sin x never equal 1.2?
Sine is never bigger than 1
Find angle x to 1 decimal place.
x = 39.0°A side of 8 cm is opposite angle x. A side of 11 cm is opposite 100°. Find x to 1 decimal place.
45.7°A side of 9 cm is opposite angle x. A side of 12 cm is opposite 78°. Find the third angle to 1 decimal place.
54.8°
Exit tickets to print
