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Teaching video
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Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Use an inverse trigonometric function with consistent angle units.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A right-triangle model rises 7 m over 24 horizontal metres. Find its angle above the horizontal.
Why this math matters
Recover a direction from component measurements and verify it with the forward trigonometric ratio. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use Euclidean geometry and the angle, parallelism, similarity, or congruence conditions stated; a sketch alone does not establish them.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Recover an angle from a measured ratio
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A right-triangle model rises 7 m over 24 horizontal metres. Find its angle above the horizontal.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
tan θ=7/24
The rise is opposite and the horizontal run adjacent to the requested angle.
Develop the calculation
θ=arctan(7/24)
The inverse function converts the ratio to an acute angle.
Check and interpret
θ≈16.26°
A degree-mode check gives tan(16.26°) approximately 0.292, consistent with the input ratio.
The result
θ≈16.26°
A degree-mode check gives tan(16.26°) approximately 0.292, consistent with the input ratio.
Common mistakes to catch
- Use degree or radian mode consistently with the requested output.
- A ratio and the angle producing it are different kinds of quantities.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Find an acute angle whose sine is 0.5.
Show a hint
Use the inverse sine in degrees.
Reveal answer and explanation
30°
sin(30°)=1/2.
Practice 2
Would arctan(24/7) give the same reference angle?
Show a hint
That reciprocal ratio swaps the two legs.
Reveal answer and explanation
No; it gives the complementary angle
The two acute angles in a right triangle sum to ninety degrees.
Take the idea with you
Recover a direction from component measurements and verify it with the forward trigonometric ratio.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Extend Pythagoras to a nonright triangle
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