Precalc 6.1 Notes.notebook
Ch. 6 Additional Topics in Trigonometry
Sec. 1
Law of Sines
Trigonometry is the study of the relationship between sides and angle of a triangle. Everything we have been doing with trig. has been centered around a right triangle. The relationship is still true if you are not dealing with a right triangle, we just need some different formulas. ­ if it is not a right triangle, it is called an oblique triangle (no right angle)
­ to solve an oblique triangle, you must know a side length and any two other parts (sides or angles)
Precalc 6.1 Notes.notebook
Law of Sines
A
­ angles are capitalized
­ sides are lower­case and opposite the angle c
b
C
a
B
­ there are three fractions, but you only use two at a time, depending on what you know of the triangle.
Precalc 6.1 Notes.notebook
Example
A
B Find the remaining angle and sides.
C
Precalc 6.1 Notes.notebook
Example
A pole tilts towards the sun at an 8 degree angle from vertical, and it casts a 22­foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43 degree. What is the length of the pole?
Precalc 6.1 Notes.notebook
The Ambiguous Case (SSA)
If the measurements of two sides and the next angle are just so, it is possible to get two different triangles with the same given information. Look at sketchpad
To know if this will happen, the sides and angle must satisfy the following...
must be acute
and where Precalc 6.1 Notes.notebook
Example
Find the triangle(s)for which a=12, b=31 and A=20.5 degrees
Precalc 6.1 Notes.notebook
Area of an Oblique Triangle
­ the equation for the area of a triangle is the area of an oblique triangle is one­half the product of the lengths of two sides times the sine of their included angle. A
c
b
C
a
B