Me. the questions is in the attachments. i will give yall 98 points. ?

a=48.7

b=51.43484959

c=112.1565686

d = 122.393202

Step-by-step 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

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step-by-step explanation: