Stephanie's Reflection

AREA OF A NON-RIGHT TRIANGLE
A=1/2(leg)(leg)sin(angle between)

EX: 2 sides of a triangle have legs 7cm and 4cm. the angle between the sides measures 73 degrees. find the area of the triangle
1/2(7)(4)sin(73)=13.388com^2

the area of triangle PQR is 15. if p is 5 and q is 10, find all possible measures of R
15=1/2(5)(10)sinR
15=25sinR
sinR=3/5
R=sin^-1(3/5)
R=36.870, 143.130

RIGHT TRIANGLES

• hypotenuse opposite angle
• a=1/2bh
• SOHCAHTOA

sin theta=opposite/hypotenuse
cos theta=adjacent/hypotenuse
tan theta=opposite/adjacent

LAW OF SINES
sinA/a sinB/b sinC/c

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

EG:
sin115/123X=sin theta/16
123sin theta=12sin115
sin theta=16sin115/123
theta=sin^-1 16sin115/123
=6.771

sin30/4=sin15/x
xsin30=4sin15
x=4sin15/sin30
x=4sin15/.5
x=2.071

A civil engineer wants to determine the distances from points A and B to an inaccessible point C. From direct measurements, AB=25cm, CA=110 and angle B=20. Find AC and BC.
sin50/25=sin20/b
bsin50=25sin20
b=25sin20/sin50
b=11.162m
sin50/25=sin110/a
asin50=25sin110
a=25sin110/sin50
a=30.667