http://www.ck12.org Chapter 4. Basic Triangle Trigonometry
Concept Problem Revisited
What if you are given the sides of a triangle are 5 and 6 and the angle between the sides isθ=π 3?
Area=^12 · 5 · 6 ·sinπ 3 ≈ 12. 99 un^2
Vocabulary
Theincluded anglebetween two sides of a triangle is the angle at the point where the two sides meet.
Guided Practice
- What is the area of∆ABCwithA= 31 ◦,b= 12 ,c=14?
- What is the area of∆XY Zwithx= 11 ,y= 12 ,z=13?
- The area of a triangle is 3 square units. Two sides of the triangle are 4 units and 5 units. What is the measure of
their included angle?
Answers:
1.Area=^12 · 12 · 14 ·sin 31◦≈ 43. 26 ...units^2 - Because none of the angles are given, there are two possible solution paths. You could use the Law of Cosines to
find one angle. The angle opposite the side of length 11 is 52. 02 ...◦therefore the area is:
Area=^12 · 12 · 13 ·sin 52. 02 ...≈ 61. 5 un^2
Another way to find the area is through the use of Heron’s Formula which is:
Area=
√
s(s−a)(s−b)(s−c)
Wheresis the semi perimeter:
s=a+b 2 +c
- 3=^12 · 4 · 5 ·sinθ
θ=sin−^1 (^34 ··^25 )≈ 17. 45 ...◦
Practice
For 1-11, find the area of each triangle.
1.∆ABCifa= 13 ,b=15, and^6 C= 70 ◦.
2.∆ABCifb= 8 ,c=4, and^6 A= 58 ◦.
3.∆ABCifb= 34 ,c=29, and^6 A= 125 ◦.
4.∆ABCifa= 3 ,b=7, and^6 C= 81 ◦.