Stephanie's Reflection

Area of a non-right triangle
A=1/2(leg)(leg)sin(angle between)
EG: The area of Triangle PQR is 15. If p is 5 and q is 10, find all possible measures of R.
A=15
P=5
Q=10
15=1/2(5)(10)sinR
15=25sinR
sinR=3/5
R=sin-1(3/5)
R≈36.870°,143.130°

Right Triangles

• A=1/2bh
• SOHCAHTOA
• sinΘ=opposite leg/hypotenuse
• cosΘ=adjacent leg/hypotenuse
• tanΘ=opposite leg/adjacent leg

Law of Sines
sinA/a - sinB/b = sinC/c

• used when you know pairs in a non-right triangle
• you are setting up proportions

Law of Cosines
(opposite leg)²=(adjacent leg)² + (other leg)² - 2(adjacent leg)(adjacent leg)cos°
EG: x, 5, 6 angle = 35°
x²=5²+6²-2(5)(6)cos35°
x=√(5²+6²-2(5)(6)cos35°)
x≈3.443

Area of Inscribed Shapes
A=nr²sinΘcosΘ