Download right triangle trig(1)work.notebook

right triangle trig(1)work.notebook
Chapter 9 ­ Right Triangle Trigonometry
You will also learn non­right triangle trigonometry
Trigonometry means the study of triangles.
A right triangle has one right angle and two complementary acute angles. The side opposite the right angle is called the hypotenuse of the right triangle. Largest side!!!
The sides opposite the acute angles are called the legs of the right triangle.
SOHCAHTOA
right triangle trig(1)work.notebook
1) Verify this a right triangle using the Pythagorean theorem.
2) Find the exact value of the following:
a) sin P
d) sin Q
b) cos P
e) cos Q
c) tan P
f) tan Q
Memorize the following:
Pythagorean Triples: Numbers that work in Pythagorean Theorem. 3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
right triangle trig(1)work.notebook
Special Right Triangles
Memorize!!
30­60­90 right triangle proportion
60
60
2
1
90
6
3
90
30
30
3√3
√3
45­45­90 right triangle proportion
45
45
√2
1
90
2√2
2
90
45
45
2
1
Homework Examples:
Triangle ABC is a right triangle. Angle C is the right angle and angle A< angle B. Find a) sin A , b) sin B, and c) sin C.
1) 16, 30, 34
2) 7, 25, 24
3) 4, 8, 4√3
right triangle trig(1)work.notebook
4) Use an equilateral triangle with sides of length 6 to find the exact values of sin 30, cos 30, and tan 60. What is the value of cos 60? How does it compare to sin 30?
What is the value of sin 60? How does it compare to cos 30?
5) An access ramp reaches a doorway that is 2.5 feet above the ground. If the ramp is 10 feet long, what is the sine of the angle that the ramp makes with the ground?
right triangle trig(1)work.notebook
Homework:
Pg 356 # 4 ­ 18 even