Given the indicated parts of triangle ABC with 𝛾 = 90°, find the exact values of the remaining parts.

Question

Given the indicated parts of triangle ABC with 𝛾 = 90°, find the exact values of the remaining parts.

a = 3

3

,   c = 6

𝛼 =	°
𝛽 =	°
b =

Answer 1

A on the left

B on the top

C on the right

RIGHT ANGLE IS B

a = BC = 3*sqrt(3)

c = AB = 6

then the hypotenus is

sqrt[ (3*sqrt(3))^2 + 6^2 ]

= sqrt[ 27+ 36]

= sqrt(63)

= sqrt(9*7)

= 3 * sqrt(7)

sin A = 3 * sqrt(3) / [ 3 * sqrt(7)]

= sqrt(3)/sqrt(7) = 0.654653670707977....

A is the inverse sine of that , which is 40.89339464913090560548252525987

B = 90 - A = 49.10660535086909439451747474013