मराठी

P In Δ A B C , i f a = 5 , b = 6 a and C = 60 ° show that its area is 15 √ 3 2 s q .units.

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

\[Given: a = 5, b = 6, c = 60°\] 

\[\text{ Area of a triangle } = \frac{1}{2}ab\sin C\]

\[ = \frac{1}{2} \times 5 \times 6 \times \sin60°= 15 \times \frac{\sqrt{3}}{2}sq . \text{ units }\]

\[\text{ Hence proved } .\]  

shaalaa.com
Sine and Cosine Formulae and Their Applications
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 10: Sine and cosine formulae and their applications - Exercise 10.2 [पृष्ठ २५]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 10 Sine and cosine formulae and their applications
Exercise 10.2 | Q 1 | पृष्ठ २५

संबंधित प्रश्‍न

If in ∆ABC, ∠A = 45°, ∠B = 60° and ∠C = 75°, find the ratio of its sides. 


In ∆ABC, if a = 18, b = 24 and c = 30 and ∠c = 90°, find sin A, sin B and sin C


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:

\[\frac{c}{a - b} = \frac{\tan\left( \frac{A}{2} \right) + \tan \left( \frac{B}{2} \right)}{\tan \left( \frac{A}{2} \right) - \tan \left( \frac{B}{2} \right)}\]

 


In triangle ABC, prove the following: 

\[\frac{c}{a + b} = \frac{1 - \tan \left( \frac{A}{2} \right) \tan \left( \frac{B}{2} \right)}{1 + \tan \left( \frac{A}{2} \right) \tan \left( \frac{B}{2} \right)}\]

 


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: 

\[b \sin B - c \sin C = a \sin \left( B - C \right)\]

 


In triangle ABC, prove the following: 

\[a \left( \sin B - \sin C \right) + \left( \sin C - \sin A \right) + c \left( \sin A - \sin B \right) = 0\]

 


In triangle ABC, prove the following: 

\[\frac{a^2 \sin \left( B - C \right)}{\sin A} + \frac{b^2 \sin \left( C - A \right)}{\sin B} + \frac{c^2 \sin \left( A - B \right)}{\sin C} = 0\]

 


In triangle ABC, prove the following:

\[\frac{\cos 2A}{a^2} - \frac{\cos 2B}{b^2} - \frac{1}{a^2} - \frac{1}{b^2}\]

 


In triangle ABC, prove the following: 

\[\frac{\cos^2 B - \cos^2 C}{b + c} + \frac{\cos^2 C - \cos^2 A}{c + a} + \frac{co s^2 A - \cos^2 B}{a + b} = 0\]

 


In triangle ABC, prove the following: 

\[a \cos A + b\cos B + c \cos C = 2b \sin A \sin C = 2 c \sin A \sin B\]

 


\[a \left( \cos B \cos C + \cos A \right) = b \left( \cos C \cos A + \cos B \right) = c \left( \cos A \cos B + \cos C \right)\]


In ∆ABC, prove that \[a \left( \cos C - \cos B \right) = 2 \left( b - c \right) \cos^2 \frac{A}{2} .\] 


In ∆ABC, if sin2 A + sin2 B = sin2 C. show that the triangle is right-angled. 


In ∆ABC, if a2b2 and c2 are in A.P., prove that cot A, cot B and cot C are also in A.P. 


At the foot of a mountain, the elevation of it summit is 45°; after ascending 1000 m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain. 


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:

\[\frac{c - b \cos A}{b - c \cos A} = \frac{\cos B}{\cos C}\] 

 


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 \[\frac{\cos A}{2} = \frac{\cos B}{7} = \frac{\cos C}{11}\] 


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. 

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 a ∆ABC, if sinA and sinB are the roots of the equation  \[c^2 x^2 - c\left( a + b \right)x + ab = 0\]  then find \[\angle C\]  

 


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 a ∆ABC, if  \[\left( c + a + b \right)\left( a + b - c \right) = ab\] then the measure of angle C 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 


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)]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×