Answer:
a=48.7
b=51.43484959
c=112.1565686
d = 122.393202
Explanation:
We can find the hypotenuse of the right triangle
sin theta = opposite/hypotenuse
sin 23.6 =49/d
Multiply d on each side
d sin23.6 =49
Divide by sin 23.6
d sin 23.6/ sin23.6 = 49/ sin23.6
d = 122.393202
We can find c using Pythagorean theorem
49^2 + c^2 =d^2
2401 + c^2= 122.393202^2
2401 + c^2=14980.09589
Subtract 2401 from each side
2401-2401 + c^2=14980.09589-2401
c^2 = 12579.09589
Take the square root of each side
sqrt(c^2) = sqrt(12579.09589)
c=112.1565686
We can find b from sin theta = opposite /hypotenuse
sin 72.3 = 49/b
Multiply b on each side
b sin72.3 =49
Divide by sin 72.3
b sin 72.3/ sin72.3 = 49/ sin72.3
b = 49/ sin72.3
b=51.43484959
The three angles of the triangle add to 180
The big angle at the top, call it A
90 +23.6 +A = 180
Combine like terms
113.6 +A = 180
Subtract 113.6 from each side
113.6-113.6+A = 180-113.6
A =66.4
The three angles of the triangle add to 180
The small angle next to a, call it a'
90 +72.3 +a' = 180
Combine like terms
162.3 +a' = 180
Subtract 162.3 from each side
162.3-162.3 +a' = 180-162.3
a' = 17.7
The angle a is the difference between A and a'
a = A - a'
a = 66.4-17.7
a=48.7