Advertisements
Advertisements
प्रश्न
In \[∆ ABC, if a = 5, b = 6 a\text{ and } C = 60°\] show that its area is \[\frac{15\sqrt{3}}{2} sq\].units.
Advertisements
उत्तर
\[Given: a = 5, b = 6, c = 60°\]
\[\text{ Area of a triangle } = \frac{1}{2}ab\sin C\]
\[ = \frac{1}{2} \times 5 \times 6 \times \sin60°= 15 \times \frac{\sqrt{3}}{2}sq . \text{ units }\]
\[\text{ Hence proved } .\]
APPEARS IN
संबंधित प्रश्न
If in ∆ABC, ∠A = 45°, ∠B = 60° and ∠C = 75°, find the ratio of its sides.
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:
\[\left( a - b \right) \cos \frac{C}{2} = c \sin \left( \frac{A - B}{2} \right)\]
In triangle ABC, prove the following:
In 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 ∆ABC, prove that: \[a \sin\frac{A}{2} \sin \left( \frac{B - C}{2} \right) + b \sin \frac{B}{2} \sin \left( \frac{C - A}{2} \right) + c \sin \frac{C}{2} \sin \left( \frac{A - B}{2} \right) = 0\]
In ∆ABC, prove that: \[\frac{b \sec B + c \sec C}{\tan B + \tan C} = \frac{c \sec C + a \sec A}{\tan C + \tan A} = \frac{a \sec A + b \sec B}{\tan A + \tan B}\]
In triangle ABC, prove the following:
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 \[∆ ABC, if a = \sqrt{2}, b = \sqrt{3} \text{ and } c = \sqrt{5}\] show that its area is \[\frac{1}{2}\sqrt{6} sq .\] units.
The sides of a triangle are a = 4, b = 6 and c = 8. Show that \[8 \cos A + 16 \cos B + 4 \cos C = 17\]
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 that \[a \left( \cos B + \cos C - 1 \right) + b \left( \cos C + \cos A - 1 \right) + c\left( \cos A + \cos B - 1 \right) = 0\]
In ∆ABC, prove the following:
\[a^2 = \left( b + c \right)^2 - 4 bc \cos^2 \frac{A}{2}\]
In ∆ABC, prove the following:
\[\sin^3 A \cos \left( B - C \right) + \sin^3 B \cos \left( C - A \right) + \sin^3 C \cos \left( A - B \right) = 3 \sin A \sin B \sin C\]
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.
In ∆ABC, if a = 8, b = 10, c = 12 and C = λA, find the value of λ.
Answer the following questions in one word or one sentence or as per exact requirement of the question.
In any triangle ABC, find the value of \[a\sin\left( B - C \right) + b\sin\left( C - A \right) + c\sin\left( A - B \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 any ∆ABC, 2(bc cosA + ca cosB + ab cosC) =
Mark the correct alternative in each of the following:
In a ∆ABC, if \[\left( c + a + b \right)\left( a + b - c \right) = ab\] then the measure of angle C is
Find the value of `(1 + cos pi/8)(1 + cos (3pi)/8)(1 + cos (5pi)/8)(1 + cos (7pi)/8)`
If x = sec Φ – tan Φ and y = cosec Φ + cot Φ then show that xy + x – y + 1 = 0
[Hint: Find xy + 1 and then show that x – y = –(xy + 1)]
