Advertisements
Advertisements
प्रश्न
Answer the following questions in one word or one sentence or as per exact requirement of the question.
In a ∆ABC, if b = 20, c = 21 and \[\sin A = \frac{3}{5}\]
Advertisements
उत्तर
In ∆ABC, b = 20, c = 21 and \[\sin A = \frac{3}{5}\]
Using cosine rule, we have
\[\cos A = \frac{b^2 + c^2 - a^2}{2bc}\]
\[ \Rightarrow \sqrt{1 - \left( \frac{3}{5} \right)^2} = \frac{{20}^2 + {21}^2 - a^2}{2 \times 20 \times 21} \left( \cos^2 A + \sin^2 A = 1 \right)\]
\[ \Rightarrow \sqrt{\frac{16}{25}} = \frac{400 + 441 - a^2}{840}\]
\[ \Rightarrow \frac{4}{5} = \frac{841 - a^2}{840}\]
\[ \Rightarrow 672 = 841 - a^2\]
\[\Rightarrow a^2 = 841 - 672 = 169\]
\[ \Rightarrow a = 13\]
संबंधित प्रश्न
If in ∆ABC, ∠C = 105°, ∠B = 45° and a = 2, then find b.
In triangle ABC, prove the following:
In triangle ABC, prove the following:
In any triangle ABC, prove the following:
In triangle ABC, prove the following:
\[\frac{a^2 - c^2}{b^2} = \frac{\sin \left( A - C \right)}{\sin \left( A + C \right)}\]
In triangle ABC, prove the following:
In triangle ABC, prove the following:
In triangle ABC, prove the following:
\[a \left( \cos B \cos C + \cos A \right) = b \left( \cos C \cos A + \cos B \right) = c \left( \cos A \cos B + \cos C \right)\]
In ∆ABC, prove that \[a \left( \cos C - \cos B \right) = 2 \left( b - c \right) \cos^2 \frac{A}{2} .\]
In ∆ABC, if a2, b2 and c2 are in A.P., prove that cot A, cot B and cot C are also in A.P.
If the sides a, b and c of ∆ABC are in H.P., prove that \[\sin^2 \frac{A}{2}, \sin^2 \frac{B}{2} \text{ and } \sin^2 \frac{C}{2}\]
In \[∆ ABC, if a = 5, b = 6 a\text{ and } C = 60°\] show that its area is \[\frac{15\sqrt{3}}{2} sq\].units.
In \[∆ ABC, if a = \sqrt{2}, b = \sqrt{3} \text{ and } c = \sqrt{5}\] show that its area is \[\frac{1}{2}\sqrt{6} sq .\] units.
In ∆ ABC, if a = 18, b = 24 and c = 30, find cos A, cos B and cos C.
In ∆ABC, prove the following: \[c \left( a \cos B - b \cos A \right) = a^2 - b^2\]
In ∆ABC, prove the following:
\[2 \left( bc \cos A + ca \cos B + ab \cos C \right) = a^2 + b^2 + c^2\]
In ∆ABC, prove the following:
\[\left( c^2 - a^2 + b^2 \right) \tan A = \left( a^2 - b^2 + c^2 \right) \tan B = \left( b^2 - c^2 + a^2 \right) \tan C\]
In ∆ABC, prove the following:
\[a^2 = \left( b + c \right)^2 - 4 bc \cos^2 \frac{A}{2}\]
In ∆ABC, prove the following:
\[4\left( bc \cos^2 \frac{A}{2} + ca \cos^2 \frac{B}{2} + ab \cos^2 \frac{C}{2} \right) = \left( a + b + c \right)^2\]
In \[∆ ABC, \frac{b + c}{12} = \frac{c + a}{13} = \frac{a + b}{15}\] Prove that \[\frac{\cos A}{2} = \frac{\cos B}{7} = \frac{\cos C}{11}\]
In \[∆ ABC, if \angle B = 60°,\] prove that \[\left( a + b + c \right) \left( a - b + c \right) = 3ca\]
If in \[∆ ABC, \cos^2 A + \cos^2 B + \cos^2 C = 1\] prove that the triangle is right-angled.
Answer the following questions in one word or one sentence or as per exact requirement of the question.
Find the area of the triangle ∆ABC in which a = 1, b = 2 and \[\angle C = 60º\]
Answer the following questions in one word or one sentence or as per exact requirement of the question.
In a ∆ABC, if \[\cos A = \frac{\sin B}{2\sin C}\] then show that c = a.
Answer the following questions in one word or one sentence or as per exact requirement of the question.
If the sides of a triangle are proportional to 2, \[\sqrt{6}\] and \[\sqrt{3} - 1\] find the measure of its greatest angle.
Answer the following questions in one word or one sentence or as per exact requirement of the question.
In any ∆ABC, find the value of
\[\sum^{}_{}a\left( \text{ sin }B - \text{ sin }C \right)\]
Mark the correct alternative in each of the following:
In any ∆ABC, \[\sum^{}_{} a^2 \left( \sin B - \sin C \right)\] =
Mark the correct alternative in each of the following:
In a ∆ABC, if a = 2, \[\angle B = 60°\] and\[\angle C = 75°\]
Mark the correct alternative in each of the following:
If the sides of a triangle are in the ratio \[1: \sqrt{3}: 2\] then the measure of its greatest angle is
Mark the correct alternative in each of the following:
In any ∆ABC, the value of \[2ac\sin\left( \frac{A - B + C}{2} \right)\] is
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`, then find the value of xy + yz + zx.
