Transcript Sec 6.2 Trigonometry of Right Triangles

Sec 6.2
Trigonometry of Right Triangles
Objectives:
•To define and use the six
trigonometric functions as ratios of
sides of right triangles.
•To solve right triangles using
trigonometric ratios.
Trigonometric Ratios
sin  
opposite
adjacent
opposite
cos  
tan  
hypotenuse
hypotenuse
adjacent
csc  
hypotenuse
hypotenuse
adjacent
sec  
cot  
opposite
adjacent
opposite
Ex 1. Find the six trig ratios of the angle .
Ex 2. Sketch a right triangle corresponding to the trig
function of the acute angle . Use the Pythagorean
theorem to find the third side and then find the other 5
trig functions.
a)
cos  
3
4
b)
csc  
13
12
Class Work
1. Find the six trig ratios of the angle .
7

6
2. a) Find sin  and cos 

b) Find tan  and cot 
c) Find sec  and csc 
4
7

3. Sketch a right triangle with acute angle  and
find the other five trig ratios of . (use
Pythagorean Thm)
7
a) cos  
8
b) tan   3
Ex 4. Find the exact value of x.
60
a)
x
13
45
x
cos 45 
13
x
13(cos 45 ) 
13
13
x  13(cos 45 )
x  9.19
b)
x
21
sin 60 
x
21
x (sin 60 ) 
x
x
21
x(sin 60 )
21

(sin 60 ) (sin 60 )
21
x
 24.25
(sin 60 )
Find the exact value of x.
5.
6.
Solving a Right Triangle
• A triangle has six parts—three angles and
three sides.
• To solve a triangle means to determine all
of its parts from the information known about
the triangle.
– In other words, we determine the lengths
of the three sides and the measures of
the three angles.
Ex 5. Solve the triangle.
a)
Class Work
Solve the triangle.
8.)
Applications Involving Right Triangles.
Ex 9.
From the top of a 200 ft lighthouse, the angle of
depression to a ship in the ocean is 23.
How far is the ship from the base of the lighthouse?
Ex 10.
A surveyor is standing 115 feet from the base of the
Washington Monument. The surveyor measures the angle
of elevation to the top of the monument as 78.3. How tall is
the Washington Monument?
HW #1 Pg. 484
(1-21, 29, 31) odd