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The law of sines worksheets Grade 11

Find a side of a triangle from two angles and a side.

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Free · Worked example · 15 problems · Answer key · US Letter

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How to do it

a ÷ sin A = b ÷ sin B. Use it when you know two angles and a side.

A =90∘,B=45∘,a =4:b=22\text{A }= 90^{\circ}, B = 45^{\circ}, \text{a }= 4:\quad b = 2\sqrt{2}
asin⁡A=bsin⁡B\dfrac{\text{a}}{\sin \text{A}} = \dfrac{b}{\sin B}the law of sines
b=4 sin⁡45∘sin⁡90∘=22b = \dfrac{4\ \sin 45^{\circ}}{\sin 90^{\circ}} = 2\sqrt{2}sin 90° = 1, sin 45° = √(2)/2

Example problems

  1. A =45∘,B=90∘,a =8:b=\text{A }= 45^{\circ}, B = 90^{\circ}, \text{a }= 8:\quad b =
  2. A =30∘,B=90∘,a =12:b=\text{A }= 30^{\circ}, B = 90^{\circ}, \text{a }= 12:\quad b =
  3. A =30∘,B=60∘,a =11:b=\text{A }= 30^{\circ}, B = 60^{\circ}, \text{a }= 11:\quad b =
  4. A =30∘,B=45∘,a =5:b=\text{A }= 30^{\circ}, B = 45^{\circ}, \text{a }= 5:\quad b =

Trigonometry

  1. Right triangle trigonometry: sin, cos and tan
  2. Special right triangles and exact trig values
  3. Converting degrees and radians
  4. The unit circle
  5. Amplitude and period
  6. The Pythagorean identity
  7. Simplifying trig expressions with identities
  8. Solving trigonometric equations
  9. The law of cosines
  10. The law of sines