Mathematics
Grade 10
15 min
Trigonometric ratios: sin, cos, and tan
Trigonometric ratios: sin, cos, and tan
What you'll learn
- Solve multi-step word problems involving addition, subtraction, multiplication, and division with at least 80% accuracy.
- Identify the operations needed to solve a multi-step word problem and explain the order in which to perform them, using keywords and prior knowledge in at least 3 out of 4 word problems.
- Apply estimation strategies to check if the answer to a multi-step word problem is reasonable in at least 2 out of 3 attempts.
- Explain the steps taken to solve a multi-step word problem clearly and completely, demonstrating understanding of the problem's context and mathematical concepts, in a written response or oral explanation.
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.
Define the sine, cosine, and tangent ratios for an acute angle in a right-angled triangle.
Calculate the exact values of sin, cos, and tan for a given angle when all three side lengths are known.
Use a scientific calculator to find the decimal approximation of sin, cos, and tan for any given angle.
Set up a trigonometric equation to find the length of an unknown side in a right-angled triangle.
Solve for an unknown side length in a right-angled triangle using the appropriate trigonometric ratio.
How can you measure the height of a skyscraper or a giant tree without a massive tape measure? 🌳 Trigonometry gives us the tools to measure the u...
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Key Concepts & Vocabulary
TermDefinitionExample
Right-Angled TriangleA triangle that has one angle measuring exactly 90 degrees. The other two angles are always acute (less than 90 degrees).A triangle with angles 30°, 60°, and 90°.
HypotenuseThe longest side of a right-angled triangle. It is always the side directly opposite the 90-degree angle.In a triangle with sides 3cm, 4cm, and 5cm, the 5cm side is the hypotenuse.
Reference Angle (θ)The specific acute angle in a right-angled triangle that we are focusing on to determine the opposite and adjacent sides.In a triangle ABC with a right angle at C, if we are focusing on angle A, then A is our reference angle.
Opposite SideThe side of the triangle that is directly across from the reference angle (θ).If our reference angle is 30°, the side that does not touch this a...
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Core Formulas
The Sine Ratio (SOH)
sin(θ) = \frac{\text{Opposite}}{\text{Hypotenuse}}
Use the sine ratio when you know or need to find the Opposite side and the Hypotenuse, relative to a known angle.
The Cosine Ratio (CAH)
cos(θ) = \frac{\text{Adjacent}}{\text{Hypotenuse}}
Use the cosine ratio when you know or need to find the Adjacent side and the Hypotenuse, relative to a known angle.
The Tangent Ratio (TOA)
tan(θ) = \frac{\text{Opposite}}{\text{Adjacent}}
Use the tangent ratio when you know or need to find the Opposite and Adjacent sides, relative to a known angle.
Mnemonic: SOH CAH TOA
SOH: Sine is Opposite over Hypotenuse. CAH: Cosine is Adjacent over Hypotenuse. TOA: Tangent is Opposite over Adjacent.
A memory aid to help you remember the three primary trigonometric...
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Challenging
In triangle ABC, the right angle is at C. Angle B is the reference angle. A student correctly identifies AC as the opposite side but incorrectly identifies AB as the adjacent side. What is the actual name for side AB, and what common pitfall does this represent?
A.AB is the adjacent side; this is not a pitfall.
B.AB is the hypotenuse; this represents mixing up Adjacent and Hypotenuse.
C.AB is the hypotenuse; this represents choosing the wrong ratio.
D.AB is the opposite side; this represents mixing up Opposite and Adjacent.
Challenging
Two buildings are 50 meters apart. From the top of the shorter building, the angle of elevation to the top of the taller building is 30°. The shorter building is 80 meters tall. What is the height of the taller building, to the nearest meter?
A.105 m
B.80 m
C.99 m
D.109 m
Easy
In a right-angled triangle, which trigonometric ratio is defined as the length of the Opposite side divided by the length of the Hypotenuse?
A.Sine (sin)
B.Cosine (cos)
C.Tangent (tan)
D.Hypotenuse (hyp)
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What grade level is "Trigonometric ratios: sin, cos, and tan"?
Trigonometric ratios: sin, cos, and tan is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Trigonometric ratios: sin, cos, and tan?
You'll be able to: Solve multi-step word problems involving addition, subtraction, multiplication, and division with at least 80% accuracy; Identify the operations needed to solve a multi-step word problem and explain the order in which to perform….
Is "Trigonometric ratios: sin, cos, and tan" free to practice?
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How many practice questions are included with Trigonometric ratios: sin, cos, and tan?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.