Can you help me with a trig question? (sin a/sin b)=2, a+b=90, find a (the angles are in degrees). Thanks!?

As given, a + b = 90°, b = 90° - a

==> sin(b) = sin(90 - a) = cos(a)

So, sin(a)/sin(b) = sin(a)/cos(a) = tan(a) = 2

So a = tan⁻¹(2) = 63.43°

sin(a) / sin(b) = 2

sin(a) = 2 * sin(b)

a + b = 90

a = 90 - b

sin(a) = sin(90 - b)

sin(a) = sin(90)cos(b) - sin(b)cos(90)

sin(a) = 1 * cos(b) - sin(b) * 0

sin(a) = cos(b)

sin(a) = 2 * sin(b)

cos(b) = 2 * sin(b)

cot(b) = 2

tan(b) = 1/2

b = arctan(1/2)

a = 90 - arctan(1/2)

Make sure your calculator is in degree mode

I get a = atan( 2) = 63.43495 degrees, plus any whole multiple of 180 degrees.

sin a = 2 sin b

a+b = 90

b= 90-a

sin a = 2 sin (90-a)

sin a = 2 ( sin(90) cos(a) - cos(90) sin(a))

sin a = 2 (cos(a) -0)

sin a = 2 cos a

sin a - 2 cos a = 0

divide both sides by cos a

tan a - 2 = 0

tan a = 2

a = tan^-1(2) = 1.10715 radians

= (1.10715)(180/pi) = 63.44 degrees

b=90-a

b= 90-63.44 = 26.56 degrees

If a + b = 90, then sin(b) = cos(a), so the first equation implies that

sin(a) = 2*cos(a) =>

sin^2(a) = 4*cos^2(a) =>

sin^2(a) = 4*(1 - sin^2(a)) =>

5*sin^2(a) = 4 =>

sin^2(a) = 4/5 =>

sin(a) = 2/sqrt(5) =>

a = 63.43 degrees, b = 26.57 degrees;

and there are some other answers involving related angles, or by switching a with b.