MATH 122/126: RIGHT TRIANGLE STUFF

In each of the following, c is the hypotenuse, γ the right angle, a the leg opposite angle α , and b the leg opposite angle β .

1. α = 45° , c = 4
   Find a, b, tan β
2. β = 60° , a = 3
   Find b, c, sin β , sec α
3. a = 5, b = 6
   Find c, sin α , tan β
4. a = x, b = 1
   Find c, sin α , tan β
5. a = 2, c = $2\sqrt{3}$
   Find b, cos α , tan α
6. c = x, a = 1
   Find b, sin α , sin β , tan β
7. b = y, c = 2
   Find a, sin α , cos α , tan β
8. α = 30° , a = x
   Find b, c, tan β

ANSWERS:

1. a = b = 2√2
       tan β = 1
2. b = 3√3
   c = 6
   sin β = √3/2
   sec α = 2√3/3
3. c = √61
   sin α = $\frac{5\sqrt{61}}{61}$
   tan β = 6/5
4. c = $\sqrt{x^2+1}$
   sin α = $\frac{x}{\sqrt{x^2+1}}$
   tan β = 1/x
5. b = 2√2
   cos α = √6/3
   tan α = √2/2
6. b = $\sqrt{x^2-1}$
   sin α = 1/x
   sin β = $\frac{\sqrt{x^2-1}}{x}$
   tan β = $\sqrt{x^2-1}$
7. a = $\sqrt{4-y^2}$
   sin α = $\frac{\sqrt{4-y^2}}{2}$
   cos α = y/2
   tan β = $\frac{y}{\sqrt{4-y^2}}$
8. b = x√3
   c = 2x
   tan β = √3