Practice Flashcards
Flip to reveal answersArea of a triangle with two sides and the included angle?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Area of a triangle
Sign up free to track progress and get spaced-repetition review schedules.
Question
Area of a triangle with two sides and the included angle?
Answer
½ab·sinC, where C is the angle between sides a and b.
Question
Which angle goes in ½ab·sinC?
Answer
The included angle — the one between the two sides you use.
Question
How do you find the included angle from a given area?
Answer
Set ½ab·sinC = Area, solve for sin C, then take sin⁻¹ (watch for the obtuse solution).
Question
Why might there be two possible included angles?
Answer
sin C = sin(180° − C), so an acute and an obtuse angle can give the same area.
Question
Area of a triangle: sides 6, 8, included angle 30°?
Answer
½(6)(8)sin30° = 12.
Question
What if the included angle isn't given?
Answer
Find it first (cosine rule from SSS, or sine rule), then use ½ab·sinC.
Question
Is ½ab·sinC ever just ½ab?
Answer
Yes, when C = 90° (sin 90° = 1) — it reduces to ½ × base × height.
Question
Common area-formula mistake?
Answer
Using a non-included angle, or forgetting the factor of ½.
Read the notes
Full study notes for Area of a triangle
Topic 3.2 hub
Sine & cosine rules
More from Topic 3.2
All flashcards in this topic
Math AA SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free