Flashcards · Maths · Further Trigonometry
Area of a Triangle and Segments
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What is the area of a triangle given two sides and the included angle?
\(\dfrac{1}{2}ab\sin C\).
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Which angle must be used in the formula?
The angle between the two sides.
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Why is the formula \(\dfrac{1}{2}ab\sin C\)?
The height is \(b\sin C\), so area is half base times height.
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What is \(\sin 30^\circ\)?
\(\dfrac{1}{2}\).
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What is \(\sin 60^\circ\)?
\(\dfrac{\sqrt{3}}{2}\).
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What is \(\sin 90^\circ\)?
1.
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What does the area become if \(C = 90^\circ\)?
\(\dfrac{1}{2}ab\).
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How do you find the angle from the area?
\(\sin C = \dfrac{2 \times \text{Area}}{ab}\).
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What is a segment of a circle?
The part between a chord and an arc.
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What is the area of a segment?
Sector minus triangle.
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What is the area of a sector?
\(\dfrac{\theta}{360} \times \pi r^2\).
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What is the area of the triangle in a sector with radius \(r\)?
\(\dfrac{1}{2}r^2\sin\theta\).
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What is the second solution of \(\sin C = \dfrac{1}{2}\)?
\(150^\circ\).
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What are the units of area?
Square units, such as cm\(^2\).
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What does exact mean?
Leaving the answer in surds and \(\pi\).
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Can you use any two sides?
Yes, with the angle between them.