Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Match corresponding sides and opposite angles in the sine rule.
- 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 triangle has A=30°, B=45°, and side a=6 opposite A. Find side b opposite B.
Why this math matters
Use an angle-side correspondence to transfer one measured length to another side. 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.
Use a known opposite side-angle pair
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A triangle has A=30°, B=45°, and side a=6 opposite A. Find side b opposite B.
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
b/sin 45°=6/sin 30°
Pair each side with its own opposite angle.
Develop the calculation
b=6(√2/2)/(1/2)
Use the two exact trigonometric values.
Check and interpret
b=6√2≈8.485
The side opposite forty-five degrees is longer than the side opposite thirty degrees.
The result
b=6√2≈8.485
The side opposite forty-five degrees is longer than the side opposite thirty degrees.
Common mistakes to catch
- Pair every side with its opposite angle.
- When an inverse sine is used with SSA data, inspect a possible supplementary solution.
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
What is the third angle in the main triangle?
Show a hint
Subtract both known angles from 180 degrees.
Reveal answer and explanation
105°
180−30−45=105.
Practice 2
Why is b/a=sin A/sin B incorrect?
Show a hint
Keep the ratios in matching order.
Reveal answer and explanation
The angle ratio must be sin B/sin A
Reversing only one pair inverts the scale factor.
Take the idea with you
Use an angle-side correspondence to transfer one measured length to another side.
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: Find area without a stated altitude
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