Properties Of Triangles — Practice Quiz
Telangana Open School (TOSS) · Class 12 · Mathematics
Try a 4-question quiz on Properties Of Triangles for Telangana Open School (TOSS) Class 12 Mathematics: tap an answer to check it and see why.
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Quick Quiz: Properties Of Triangles
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In any triangle ABC, what is the value of $\frac{a}{\sin A}$ equal to?
If in a triangle ABC, $a = 2R \sin A$, then what is the value of $\sin A$?
Which of the following represents the projection formula for side $a$?
What is the formula for $\cos A$ in terms of the sides of triangle ABC?
Sample Questions
If $\angle A = 60^\circ$, $b = 3$, $c = 4$, what is the value of $a^2$ using the cosine rule?
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13
Using $a^2 = b^2 + c^2 - 2bc \cos A$, we get $a^2 = 9 + 16 - 2(3)(4)(0.5) = 25 - 12 = 13$.
Which formula is used to find the area of a triangle when all three sides are known?
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Heron’s formula
Heron’s formula $\Delta = \sqrt{s(s-a)(s-b)(s-c)}$ is used when all three sides are known and $s = \frac{a+b+c}{2}$.
In a triangle, if $a = b$, then which of the following is true?
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∠A = ∠B
If two sides of a triangle are equal, then the angles opposite to them are also equal. So $a = b \Rightarrow \angle A = \angle B$.
What is the value of $\sin \frac{A}{2}$ in terms of the semi-perimeter $s$?
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√[(s−b)(s−c)/bc]
The half-angle formula for sine is $\sin \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{bc}}$.
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