Transcript 5.2/5.3 Apply the sine, cosine and tangent ratios

5.2 and 5.3
Apply the sine, cosine and
tangent ratios
HW Quiz: Wednesday
5.1-5.4 Quiz: Friday!
Special Triangles Test: Aug. 27
Complementary Angles
• Two angles are complementary angles
if the sum of their measures is 90o
Trigonometry
• Is a branch of mathematics that deals
with the relationships between the
sides and angles of triangles and the
calculations based on these
relationships.
• A trigonometric ratio:
– Is a ratio of the lengths of two sides in a
right triangle.
Sine and Cosine
Ratios
• Let ΔABC be a right triangle with acute A.
The sine of A and cosine of A (written as
sinA and cosA) are defined as follows:
length of leg opposite A BC
sin A 

length of hypotenuse
AB
cos A 
length of leg adjacent A AC

length of hypotenuse
AB
B
C
A
Tangent Ratio
• Let ΔABC be a right triangle with acute A.
The tangent of A (written as tanA) is defined
as follows:
length of leg opposite A
BC
tan A 

length of leg adjacent to A AC
B
C
A
Example 1:
• Find the sine, cosine, and tangent ratio
for x and y.
Example 2:
• Find the height h of the lamppost to the
nearest inch.
Example 3:
• Find the value of x. Round to the
nearest tenth.
Example 4:
• Find the height and length of the base
of the ramp shown.
Example 5:
• Find the value of x. Round to the
nearest tenth.
Homework:
p. 161 2-12 even, 21-23
p. 167 25-26
p. 168 2-12 even (omit 8)