NO CALCULATOR ALLOWED Solve the triange Round lengths to the

**NO CALCULATOR ALLOWED: Solve the triange. Round lengths to the nearest tenth and angle measures to the nearest degree. a=6, c=10, B=125 degrees ***I know how to do this because you use the Law of Cosines, but my test is tomorrow and we are NOT allowed to use a calculator of any type, everything has to be by hand. So how do you calculate it without a calculator?

Solution

solution-

you know the process but you dont know how to estimate the angle

the procedure is as follows-

B=125

cosB =cos125=-sin35

sin35 can be approximate as -

sin35=sin(30+5)= sin30cos5+cos30sin5

now

we know that-

for small angle x

sinx is nearly equal to x

where x is in radian

now

5deg =pi/180*5radian= 3.14*5/180=0.087

and for small angle cosx is nearly equal to 1

hence

cos0.087=cos5deg=1

now

we was approximating   sin35=sin(30+5)= sin30cos5+cos30sin5=(1/2)*1+(sqrt3/2)*0.087

on solving it comes 0.575 which is closer to actual value (0.574)

hence

cos125=-sin35=-0.574

now with this value every parameter of triangle can be calculated.