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HW-pg. 529-530 (3-20, 37-43)
5.8, 8.2-8.3 quiz WEDNESDAY 2-12-14
www.westex.org HS, Teacher Website
2-7-14
Warm up—Geometry H
Go over HW
GOAL:
I will be able to:
1. find the sine, cosine, and tangent of an acute
angle.
HW-pg. 529-530 (3-20, 37-43)
5.8, 8.2-8.3 quiz WEDNESDAY 2-12-14
www.westex.org
HS, Teacher Website
Name _________________________
Geometry H
8.2 Trigonometric Ratios
GOAL:
I will be able to:
1. find the sine, cosine, and tangent of an acute angle.
Date ________
By the AA Similarity Postulate, a right triangle with a given acute angle is similar to every
other right triangle with that same acute angle measure. So ∆ABC ~ ∆DEF ~ ∆XYZ, and
. These are trigonometric ratios. A _______________ __________ is a ratio of
two sides of a right triangle.
Example 1: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest
hundredth.
a. sin J
b. cos J
c. tan K
YOU TRY:
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest
hundredth.
a. cos A
b. tan B
c. sin B
Example 2: Finding Trigonometric Ratios in Special Right Triangles
Use a special right triangle to write cos 30° as a fraction.
YOU TRY:
Use a special right triangle to write tan 45° as a fraction.
Example 3: Calculating Trigonometric Ratios
(CALC. MUST BE in DEGREES!!!)
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
a. sin 52°
b. cos 19°
c. tan 65°
YOU TRY:
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
a. tan 11°
b. sin 62°
c. cos 30°
The hypotenuse is always the longest side of a right triangle. So the denominator of a sine or
cosine ratio is always greater than the _______________. Therefore the sine and cosine of
an acute angle are always positive numbers less than ___. Since the tangent of an acute angle
is the ratio of the lengths of the legs, it can have _______ __________ greater than 0.
Example 4: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth.
a. BC
b. QR
a. DF
YOU TRY:
b. ST
c. BC
c. FD
d. JL
Example 5: Problem-Solving Application
The Pilatusbahn in Switzerland is the world’s steepest cog railway. Its steepest section
makes an angle of about 25.6º with the horizontal and rises about 0.9 km. To the
nearest hundredth of a kilometer, how long is this section of the railway track?
YOU TRY:
Find AC, the length of the ramp, to the nearest hundredth of a foot if the angle of
elevation is 4.8o and the height of the ramp is 1.2 ft.
8.2 Practice
Use a special right triangle to write each trigonometric ratio as a fraction.
1. sin 60°
2. cos 45°
Use your calculator to find each trigonometric ratio. Round to the nearest hundredth.
3. tan 84°
4. cos 13°
Find each length. Round to the nearest tenth.
5. CB
6. AC
Use your answers from Items 5 and 6 to write each trigonometric ratio as a fraction and
as a decimal rounded to the nearest hundredth.
7. sin A
8. cos A
9. tan A