Question
The sides of a triangle are
and
for some
.Then the greatest angle of the triangle is
- 600
- 1500
- 1200
- 900
Hint:
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
The correct answer is: 1200
The sides of a triangle are
and
for some
.
![I n space increment A B C comma space
L e t space s i d e space a comma space b space a n d space c space t h e n space a equals sin alpha comma space b equals cos alpha comma space c equals square root of 1 plus sin alpha cos alpha end root
bold italic W bold italic e bold space bold italic k bold italic n bold italic o bold italic w bold space bold italic t bold italic h bold italic a bold italic t bold space bold italic t bold italic h bold italic e bold space bold italic a bold italic n bold italic g bold italic l bold italic e bold space bold italic o bold italic p bold italic p bold italic o bold italic s bold italic i bold italic t bold italic e bold space bold italic t bold italic o bold space bold italic t bold italic h bold italic e bold space bold italic l bold italic o bold italic n bold italic g bold italic e bold italic s bold italic t bold space bold italic s bold italic i bold italic d bold italic e bold space bold italic w bold italic i bold italic l bold italic l bold space bold italic h bold italic a bold italic v bold italic e bold space bold italic t bold italic h bold italic e bold space bold italic l bold italic a bold italic r bold italic g bold italic e bold italic s bold italic t bold space bold italic v bold italic a bold italic l bold italic u bold italic e bold.
bold italic S bold italic o bold comma bold space bold cos bold space bold italic C bold space bold equals bold space fraction numerator bold a to the power of bold 2 bold plus bold b to the power of bold 2 bold minus bold c to the power of bold 2 over denominator bold 2 bold a bold b end fraction
space cos space C space equals space fraction numerator sin squared alpha plus c o straight s squared straight alpha minus 1 minus sin alpha cos alpha over denominator 2 sin straight alpha cos straight alpha end fraction space space space space left curly bracket space bold italic W bold italic e bold space bold italic k bold italic n bold italic o bold italic w bold space bold italic t bold italic h bold italic a bold italic t bold space bold semicolon bold space bold italic s bold italic i bold italic n to the power of bold 2 bold space bold italic theta bold space bold plus bold space bold italic c bold italic o bold italic s to the power of bold 2 bold space bold italic theta bold space bold equals bold space bold 1 right curly bracket
cos space C space equals space fraction numerator negative sin alpha cos alpha over denominator 2 sin straight alpha cos straight alpha end fraction bold rightwards double arrow cos space C space equals space fraction numerator negative 1 over denominator 2 end fraction
cos space C space equals space fraction numerator negative 1 over denominator 2 end fraction space o r space A n g l e space C space equals 120 degree space
s o comma space G r e a t e s t space a n g l e space i s space C space I n space increment A B C. space 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)
![img](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/946689/1/961838/Screenshot%20%28233%29.png)
![img](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/946689/1/961838/Screenshot%20%28233%29.png)
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)
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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,iVBORw0KGgoAAAANSUhEUgAAAK4AAAAQCAYAAACPzETrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAtdJREFUeNrtmjFoFEEUhodDJEUIiKQIImksgkUISBARO6sgYmMhwSIEROQQCYJFCCIiHBYWdiIiFiKIpApBEAlySLAJh4WEQAqLEI40cojIcRDfw39hHebt7O3N3r4Bf/jh2JvZ/W733c57b9eY8nSL3DD61ABbbNyxsvuYVWmavKmY7zMYY+OOlV1iDq5L5MMBQWcUX/wz5KZC7l/kWqTsRZiDapT8bYDAncFJ1K4mTqgW7lPkr5GyF2EOrmfkxQEC9zG5HkHg3rbywaq5r5DfRMpehDmozpM/4nNW4C6Tv5N7GHcv9d178oUC80KJl9oH5Da5S26RJx3jzqV+qwbu+zgOs++Tf5M3yBMRsCcrNf+B9nDeV8nHMpiD6SiWqklP4PKJeI7xLnWE73zzQmmN/BQnjYP4Le5mrt/bUcTNnLsIrIT9iXAX1sbOQbtFfkQew/HuolaSmNM6zOHMtkXd2plUeF3M2E+v4LwQuoYASOsVeU4Y31XCzdohn7a2jWVcbE3sDdwsfOqGPvC0I7mXAvcq/l2X+wxc37wQ/8ANLElpfRJShbwXfxjcNXQUbI0MGLjDYj+w0oKhBe4XVLV5Atcg72oiUEZzpgq+eWW0k/jzz4zUqKOE+yz27ctlNbLP5mx1lZIqFJk0gpz4urX9A4o80+e8EDpwFJtbwlg7KKrk5hTnpWP7EnlFOfscCjGfSivOTB933EQvyPMF2mGueSG0h4uUiC/6O2FsHawauDk/XBCK5Qnl7Nyb3c4xzmauLHB5ieAHFcet7b5muDQvhB6av33oGvLa1+R1YWy/TfwyuVdRnCWF1AlsW4iAndVCR+EICso7jhWg9AcQWYH7A9t7yJmmhLmb5t9n03nnhdAyOgsruPu2He0w6RFkVdxtFFA7OFZLaOFpZGedRBHcwyqxmJNZnTS98DEutIn+v2RTPbNK3TQ6Xw/kPOtGhNyxsvuYC+kPiEEjVD5ArgIAAAEIdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1uPjQ8L21uPjxtaT5zPC9taT48bW8+KDwvbW8+PG1pPnM8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmE8L21pPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPnM8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmI8L21pPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPnM8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmM8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PC9tYXRoPp5scUAAAAAASUVORK5CYII=)
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.