Download Trigonometric Ratios

Name ____________________________________________________ Date ___________
Geometry
Ms. Parent/Mr. Viscardi
Trigonometric Ratios
The word trigonometry comes from two Greek terms, trigon, meaning triangle,
and metron, meaning measure. The study of trigonometry involves triangle
measurement.
A RATIO of the lengths of sides of a right triangle is called a trigonometric
ratio. The three most common trigonometric ratios are sine, cosine, and
tangent.
In Words
sine of  A =
measure of leg opposite
cosine of  A =
Symbols
A
sin A =
measure of hypotenuse
measurement of leg adjacent
tangent of  A =
A
cos A =
measure of hypotenuse
measure of leg opposite  A
measurement of leg adjacent  A
tan A =
Diagrams
𝐵𝐶
𝐴𝐵
𝐴𝐶
𝐴𝐵
𝐵𝐶
𝐴𝐶
Each of these three trigonometric ratios can be done to EITHER ACUTE ANGLE
in the right triangle. It CANNOT be done with the right angle.
SOH – CAH – TOA
Example 1: Find sine, cosine, and tangent ratios.
Find sin R, cos R, and tan R.
Express ratio as a fraction and as a decimal.
sin R =
cos R =
tan R =
Example 2: Use a calculator to evaluate expressions.
Use a calculator to find each value to the nearest ten thousandth.
a) cos 39° ≈
b) sin 67° ≈
You can use trigonometric ratios to find the missing measures of a right
triangle if you know the measures of two sides of a triangle or the
measure of one side and one acute angle.
Example 3: Use trigonometric ratios to find a length
Given the diagram to the right, find x. Round to the nearest yard.
Example 4: Use trigonometric ratios to find an angle.
Given the diagram to the right, find x. Round to the nearest degree.
Try the following on your own.
1. Use ∆𝐴𝐵𝐶 to find sin A, cos A, tan A, sin B, cos B, and tan B. Express each
ratio as a fraction and as a decimal to the nearest hundredth.
sin A =
sin B =
cos A =
cos B =
tan A =
tan B =
2. Use your calculator to find each value. Round to nearest hundredth.
a) sin 57°
b) cos 60°
c)
tan 30°
3. Use your calculator to find angle B. Round to the nearest degree.
a) sin B = 0.7245
b) cos B = 0.2493
c) tan B = 0.4279
Name ____________________________________________________ Date ____________
Geometry
Ms. Parent/Mr. Viscardi
Intro to Trig Homework
Find x. Round to the nearest tenth.
1.
2.
4.
5.
3.
6.
7. A plane is one mile above sea level when it begins to climb at a constant angle of 3°
for the next 60 ground miles. About how far above sea level is the plane after its
climb?
8. To guard against a fall, a ladder should make an angle of 75° or less with the
ground.
a) What is the maximum height that a 20-foot ladder can
reach safely?
b) How far from the building is the base of the ladder at the
maximum height?
9. A rock dropped from the Leaning Tower of Pisa falls to a point 14 feet from its
base. If the tower is 182 feet tall, at what angle does it lean at the ground?
10. Sonar on a destroyer detects a submarine at a depth of 200 m. If the angle is 31°,
how far apart are the two vessels?