Solving Right Triangles

Question

Suppose a = 7 and c = 9.

find b ,A ,B

Answer 1

Pythagorean Theorem:

a^2 + b^2 = c^2

so 7^2 + b^2 = 9^2

b^2 = 32

b = 5.66

sin A = a/c = 7/9

A = arcsin(7/9) = 51.06

C = 90 (right triangle)

B = 180 - 90 - 51.06 = 38.94

Answer 2

Right triangle ACB

angle ACB is the right angle at C

BC = a = 7

AC = b

AB=c = 9

then pythagorean says b = AC = sqrt( 81 - 49)

= sqrt( 32)

= 4 * sqrt(2)

for x = angle BAC, sin x = 7/9

x = arcsin(7/9)

= 51.057558731018617261508001320075

for y = angle CBA , sin y =4 * sqrt(2)/9

y = arcsin( 4*sqrt(2)/9) = 38.942441268981382738491998679925

and they add up to 90, so everything is correct