8.7: Trigonometric Ratios with a Calculator
What if you wanted to find the missing sides of a right triangle with angles of
Watch This
CK12 Foundation: Chapter8TrigonometricRatioswithaCalculatorA
James Sousa: Determining Trigonometric Function Values on the Calculator
Guidance
The trigonometric ratios are not dependent on the exact side lengths, but the angles. There is one fixed value for every angle, from
Example A
Find the trigonometric value, using your calculator. Round to 4 decimal places.
a)
b)
c)
Depending on your calculator, you enter the degree and then press the trig button or the other way around. Also, make sure the mode of your calculator is in DEGREES.
a)
b)
c)
Example B
Find the value of each variable. Round your answer to the nearest tenth.
We are given the hypotenuse. Use sine to find
Example C
Find the value of each variable. Round your answer to the nearest tenth.
We are given the adjacent leg to
Any time you use trigonometric ratios, use only the information that you are given. This will result in the most accurate answers.
Watch this video for help with the Examples above.
CK12 Foundation: Chapter8TrigonometricRatioswithaCalculatorB
Concept Problem Revisited
Use trigonometric ratios to find the missing sides. Round to the nearest tenth.
Find the length of
Vocabulary
Trigonometry is the study of the relationships between the sides and angles of right triangles. The legs are called adjacent or opposite depending on which acute angle is being used. The three trigonometric (or trig) ratios are sine, cosine, and tangent.
Guided Practice
1. What is
2. Find the length of the missing sides and round your answers to the nearest tenth: .
3. Find the length of the missing sides and round your answers to the nearest tenth: .
Answers:
1. Using your calculator, you should find that
2. Use tangent for
3. Use tangent for
Practice
Use your calculator to find the value of each trig function below. Round to four decimal places.

sin24∘ 
cos45∘ 
tan88∘ 
sin43∘ 
tan12∘ 
cos79∘ 
sin82∘
Find the length of the missing sides. Round your answers to the nearest tenth.
 Find
sin80∘ andcos10∘ .  Use your knowledge of where the trigonometric ratios come from to explain your result to the previous question.
 Generalize your result to the previous two questions. If
sinθ=x , thencos?=x .  How are
tanθ andtan(90−θ) related? Explain.
Hypotenuse
The hypotenuse of a right triangle is the longest side of the right triangle. It is across from the right angle.Legs of a Right Triangle
The legs of a right triangle are the two shorter sides of the right triangle. Legs are adjacent to the right angle.Trigonometric Ratios
Ratios that help us to understand the relationships between sides and angles of right triangles.Image Attributions
Description
Learning Objectives
Here you'll learn how to solve for missing sides in right triangles that are not one of the special right triangles.