Mathematics
Grade 10
15 min
Trigonometric ratios: find the length of a side
Trigonometric ratios: find the length of a side
What you'll learn
- Identify the overlapping and non-overlapping regions in a Venn diagram with at least 80% accuracy.
- Solve word problems involving two sets of data by accurately placing information into a Venn diagram and answering related questions with 100% accuracy.
- Explain how a Venn diagram visually represents the relationships (similarities and differences) between two groups with clear and concise language in a written response.
- Apply Venn diagrams to sort and categorize a set of objects or numbers based on two given criteria with 90% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the hypotenuse, opposite, and adjacent sides of a right-angled triangle with respect to a given acute angle.
Recall and state the three primary trigonometric ratios: sine, cosine, and tangent (SOH CAH TOA).
Select the appropriate trigonometric ratio to use based on the given side and angle information.
Set up a correct trigonometric equation to model a problem.
Algebraically solve the trigonometric equation for an unknown side length.
Use a scientific calculator to correctly evaluate trigonometric functions and find a final answer.
How can you find the height of a giant tree or a skyscraper without actually climbing it? 🌳
In this tutorial, you will learn how to use the powerful tools of trigonometry—sine, cosine, and tangent—to find the missing...
2
Key Concepts & Vocabulary
TermDefinitionExample
Right-Angled TriangleA triangle that has one angle measuring exactly 90 degrees.A triangle with angles 30°, 60°, and 90°.
Reference Angle (θ)The specific acute angle (less than 90°) in a right-angled triangle that we are focusing on for our calculations.In a problem stating 'from a 40° angle of elevation', the reference angle θ is 40°.
HypotenuseThe longest side of a right-angled triangle. It is always the side directly opposite the 90-degree angle.In a triangle with sides 3, 4, and 5, the side with length 5 is the hypotenuse.
Opposite SideThe side directly across from the reference angle (θ). Its identity depends on which acute angle you choose.If your reference angle is 30°, the side across from that angle is the 'opposite' side.
Adjacent SideTh...
3
Core Formulas
The Sine Ratio (SOH)
\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}
Use this ratio when you know or need to find the Opposite side and the Hypotenuse, relative to the reference angle θ.
The Cosine Ratio (CAH)
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}
Use this ratio when you know or need to find the Adjacent side and the Hypotenuse, relative to the reference angle θ.
The Tangent Ratio (TOA)
\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}
Use this ratio when you know or need to find the Opposite and Adjacent sides, relative to the reference angle θ.
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
An isosceles triangle has two equal sides of length 20 cm. The angle between these two sides is 40°. What is the length of the third side (the base), rounded to one decimal place?
A.13.7 cm
B.15.3 cm
C.18.8 cm
D.30.6 cm
Challenging
In right triangle ABC, angle A = 30° and the hypotenuse is 10. In right triangle XYZ, angle X = 60° and the hypotenuse is 10. Let 'b' be the side opposite angle A in triangle ABC, and 'y' be the side opposite angle X in triangle XYZ. Which statement is true?
A.b = y
B.b < y
C.b > y
D.The relationship cannot be determined.
Easy
In the mnemonic SOH CAH TOA, what does 'SOH' stand for?
A.Sine = Opposite / Hypotenuse
B.Sine = Opposite / Adjacent
C.Sine = Adjacent / Hypotenuse
D.Sine = Hypotenuse / Opposite
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Trigonometry
Mathematics for other grades
Frequently asked questions
What grade level is "Trigonometric ratios: find the length of a side"?
Trigonometric ratios: find the length of a side is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Trigonometric ratios: find the length of a side?
You'll be able to: Identify the overlapping and non-overlapping regions in a Venn diagram with at least 80% accuracy; Solve word problems involving two sets of data by accurately placing information into a Venn diagram and answering related….
Is "Trigonometric ratios: find the length of a side" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Trigonometric ratios: find the length of a side?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.