Question
The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles if the side "a" is 1, then the angle A is
Hint:
if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c . In this question, we have to find value of if the side "a" is 1, then the angle A = ?.
The correct answer is: ![straight pi over 6](data:image/png;base64,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)
![T h e space a n g l e s space o f space t h e space t r i a n g l e space A B C space a r e space d e n o t e d space b y space A comma space B comma space C space a n d space t h e space c o r r e s p o n d i n g space o p p o s i t e space s i d e s space b y space a comma space b comma space c.
s o space W e space k n o w space t h a t comma space
fraction numerator a over denominator sin space A end fraction space equals space fraction numerator b over denominator sin space B end fraction space equals space fraction numerator c over denominator sin space C end fraction space equals 2 R](data:image/png;base64,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If a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c
A.M of the sines of its angles = ![fraction numerator sin A space plus space sin B space plus space sin c over denominator 3 end fraction](data:image/png;base64,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)
According to question, The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles.
so, a + b + c = 6 x ![fraction numerator sin A space plus space sin B space plus space sin c over denominator 3 end fraction](data:image/png;base64,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)
a + b + c = 2 x (
) {
}
![space a space plus space b space plus space c space equals space space left parenthesis a over R space plus space b over R space plus c over R right parenthesis space space
s o comma space R equals 1
w e space k n o w space fraction numerator a over denominator 2 R end fraction space equals space sin A space left curly bracket space G i v e n space t h a t space a equals 1 space right curly bracket
1 half space equals space sin A space s o comma space A equals space straight pi over 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If a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c
A.M of the sines of its angles =
According to question, The perimeter of a Δ ABC is 6 times the A.M of the sines of its angles.
so, a + b + c = 6 x
a + b + c = 2 x (
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
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A triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.
Consider a body as shown in figure, consisting of two identical bulls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?
![](data:image/png;base64,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)
Consider a body as shown in figure, consisting of two identical bulls, each of mass M connected by a light rigid rod. If an impulse J=MV is imparted to the body at one of its ends, what would be its angular velocity. What is V ?
![](data:image/png;base64,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)
11H2 1H and 3 1H will have the same
11H2 1H and 3 1H will have the same
The sides of a triangle are
and
for some
.Then the greatest angle of the triangle is
The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square of one side of the triangle, is equal to a2 + b2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.
![law of cosines](https://www2.clarku.edu/~djoyce/trig/lawofcosines.jpg)
The sides of a triangle are
and
for some
.Then the greatest angle of the triangle is
The law of cosines generalizes the Pythagorean formula to all triangles. It says that c2, the square of one side of the triangle, is equal to a2 + b2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.
![law of cosines](https://www2.clarku.edu/~djoyce/trig/lawofcosines.jpg)
A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits 0 is
A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits 0 is
A uniform rod of length 2 L is placed with one end in contact with horizontal and is then inclined at an angle
to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be.....
A uniform rod of length 2 L is placed with one end in contact with horizontal and is then inclined at an angle
to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be.....
If the sides of a triangle are in the ratio then greatest angle is
If the sides of a triangle are in the ratio then greatest angle is
A straight rod of length L has one of its ends at the origin and the other end at x=L If the mass per unit length of rod is given by Ax where A is constant where is its center of mass.
A straight rod of length L has one of its ends at the origin and the other end at x=L If the mass per unit length of rod is given by Ax where A is constant where is its center of mass.
In
then ![4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals](data:image/png;base64,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)
s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.
In
then ![4 s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis equals](data:image/png;base64,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)
s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.