हिंदी

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. - Mathematics

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. 

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 10: Sine and cosine formulae and their applications - Exercise 10.2 [पृष्ठ २५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 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. 


If in ∆ABC, ∠C = 105°, ∠B = 45° and a = 2, then find b


In triangle ABC, prove the following: 

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

 


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: 

\[a^2 \left( \cos^2 B - \cos^2 C \right) + b^2 \left( \cos^2 C - \cos^2 A \right) + c^2 \left( \cos^2 A - \cos^2 B \right) = 0\]

 


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: 

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

 


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


In ∆ABC, prove that if θ be any angle, then b cosθ = c cos (A − θ) + a cos (C + θ). 


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


The upper part of a tree broken by the wind makes an angle of 30° with the ground and the distance from the root to the point where the top of the tree touches the ground is 15 m. Using sine rule, find the height of the tree. 


A person observes the angle of elevation of the peak of a hill from a station to be α. He walks c metres along a slope inclined at an angle β and finds the angle of elevation of the peak of the hill to be ϒ. Show that the height of the peak above the ground is \[\frac{c \sin \alpha \sin \left( \gamma - \beta \right)}{\left( \sin \gamma - \alpha \right)}\] 


In ∆ABC, prove the following: \[b \left( c \cos A - a \cos C \right) = c^2 - a^2\]


In ∆ABC, prove the following: \[c \left( a \cos B - b \cos A \right) = a^2 - b^2\]


In ∆ABC, prove the following

\[\left( c^2 - a^2 + b^2 \right) \tan A = \left( a^2 - b^2 + c^2 \right) \tan B = \left( b^2 - c^2 + a^2 \right) \tan C\] 

 


If in \[∆ ABC, \cos^2 A + \cos^2 B + \cos^2 C = 1\] prove that the triangle is right-angled. 

 


Two ships leave a port at the same time. One goes 24 km/hr in the direction N 38° E and other travels 32 km/hr in the direction S 52° E. Find the distance between the ships at the end of 3 hrs. 


Answer  the following questions in one word or one sentence or as per exact requirement of the question.In a ∆ABC, if b =\[\sqrt{3}\] and \[\angle A = 30°\]  find a

   

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. 

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 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 a ∆ABC, if a = 2, \[\angle B = 60°\]  and\[\angle C = 75°\] 

 


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 triangle ABC, a = 4, b = 3, \[\angle A = 60°\]   then c is a root of the equation 


Mark the correct alternative in each of the following:

In any ∆ABC, \[a\left( b\cos C - c\cos B \right) =\]  


Find the value of `(1 + cos  pi/8)(1 + cos  (3pi)/8)(1 + cos  (5pi)/8)(1 + cos  (7pi)/8)`


If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`, then find the value of xy + yz + zx.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×