How do you find the missing sides of a triangle given sides are x and 6 root 3, angles are 60 and 90?

Question

1553 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-25T15:44:32

Missing sides and angles are

#color(indigo )(x = a = 9, c = 5.1962, hat C = 30^@#

Given : #a = x, b = 6sqrt3 = 10.3923, hatA = 60^@, hat B = 90^@#

enter image source here

Applying law of sines,

#a / sin A = b / sin B = c / sin C#

#a = x = (b sin A) / sin B = (6sqrt3 * sin (60) ) / sin (90) #

#a =( 6 sqrt3 * sqrt3) / 2 = 9#

Third angle #hat C = 180 - 90 - 60 = 30^@#

enter image source here

As the angles of the right triangle are #60 : 90 : 30#, sides will be in the ratio #sqrt3 : 2 : 1#

Third side #c = (1/2) b = (1/2) * 6sqrt3 = 5.1962#