Download Use Trigonometric ratios to solve for an acute angle in a triangle

Discovering Geometry 2012-2013
12.1 Day 2 Notes
Use Trigonometric ratios to solve for an acute angle in a triangle
If you know two sides in a right triangle, you can find either acute angle.
To find m B, determine the trig ratio
A
you can use with the given sides:
When finding an angle
in a trig equation, you
will always use the key
17
9
2nd
B
C
m B
Find an angle in a trigonometric equation without a picture.
Ex1 tan x = 3.4
Ex2 sin x =
18
23
Ex3 cos x =
Find an angle in a trigonometric equation with a picture.
Ex4 Find m B.
Ex5 Find m A.
B
23
15
C
19
46
A
C
A
B
1
7
INV
Comparison: Finding a side vs. finding an angle in a right triangle using trigonometry
To find a side you must be given:
To find an angle you must be given:
- one acute angle measurement
- two side lengths
- one side length
A
D
13
50
5
E
B
C
BC
F
9
m D
Solve for x, y, and z in the right triangle. Round decimals to the nearest tenth.
11
x
1.
2.
x
3.
18
y
37˚
y
z
x
24˚
22
z
z
y
33
A Regular Polygon is a polygon where ALL _____________ and _______________ are congruent.
Sum of Interior Angles ____________________
Single Interior Angle _____________
Ex 1. Name the regular polygon and find the measure of each interior angle.
Radius (of a polygon): A segment that joins the center of a polygon and one of the vertices
 The radius ALWAYS ______________ the angle it intersects.
Find the center of each polygon and draw the radius of each polygon above.
Apothem: A segment that joins the center of a polygon and the midpoint of a side
 The apothem ALWAYS ______________ the side it intersects.
In a different color than you used for the radius, find the midpoint of a side and draw the apothem of each
polygon above.
Ex 2 Find the side, half side, and apothem lengths of the regular polygons.
c.
Side: __________.
14
d.
Side: __________
9
½ Side: _________
½ Side: ________
Apothem: ________
Apothem:_______
Mixed Review:
1. Find the m S
2.Find the area of each triangle.
Round your final answer to the nearest tenth.
T
20
14.3
R
S
24.59
53
49
41