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In triangle ABC

Right at B 

AB=35

AC=50

Find CB 

and find Angle C 

 Jun 11, 2019

Best Answer 

 #1
avatar+8437 
+3

 

By the Pythagorean Theorem,

 

352 + ( CB )2  =  502

                                         Subtract  352  from both sides of the equation.

( CB )2  =  502 - 352

                                         Simplify the right side of the equation.

( CB )2  =  1275

                                         Since  CB  is a length, take the positive square root of both sides.

CB  =  √[ 1275 ]

                                         And we can simplify the radical.

CB  =  5√[ 51 ]

                                         To get an approximate solution, plug it into a calculator.

CB  ≈  35.707

 

sin( angle )  =  opposite / hypotenuse

 

sin( C )  =  35 / 50

                                         Take the inverse sine of both sides of the equation.

C  =  arcsin( 35 / 50 )

                                         Plug  arcsin(35/50)  into a calculator to get...

C  ≈  44.427°

 Jun 11, 2019
 #1
avatar+8437 
+3
Best Answer

 

By the Pythagorean Theorem,

 

352 + ( CB )2  =  502

                                         Subtract  352  from both sides of the equation.

( CB )2  =  502 - 352

                                         Simplify the right side of the equation.

( CB )2  =  1275

                                         Since  CB  is a length, take the positive square root of both sides.

CB  =  √[ 1275 ]

                                         And we can simplify the radical.

CB  =  5√[ 51 ]

                                         To get an approximate solution, plug it into a calculator.

CB  ≈  35.707

 

sin( angle )  =  opposite / hypotenuse

 

sin( C )  =  35 / 50

                                         Take the inverse sine of both sides of the equation.

C  =  arcsin( 35 / 50 )

                                         Plug  arcsin(35/50)  into a calculator to get...

C  ≈  44.427°

hectictar Jun 11, 2019
 #2
avatar
+2

Thank you! 

Guest Jun 11, 2019
 #3
avatar
+2

Oh that was a simple and small great solution!!

I actually did a long one using the Law of cosines

Since I have all three side lengths 

therefore AB^2=AC^2 + CB^2 -2AC*BC*Cos(angle c) 

i also got to the result 44.4

Guest Jun 11, 2019

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