Question

I need help with this practice I attempted this previously my answer is in the box

Answer 1

Step-by-step explanation

Since we have the △CDE,let's represent the triangle:

We can apply the law of sines to get the value of the angle C, and then by the Sum of Interior Angles of a Triangle Theorem, we can get the value of the angle D as shown as follows:

`(\sin C)/(DE)=(\sin E)/(CD)`

Substituting terms:

`(\sin C)/(5)=(\sin 83)/(12)`

Isolating sin C:

`\sin C=5\cdot(\sin 83)/(12)`

Applying sin^-1 to both sides:

`C=\sin ^(-1)(5\cdot(\sin 83)/(12))`

Computing the terms:

`C=\sin ^(-1)(0.4135)`

Computing the argument:

`C=24.43\text{ degre}es`

Finally, by applying the Sum of Interior Angles of a Triangle Theorem, we can get the value of D as shown as follows:

C + D + E = 180

24.43 + D + 83 = 180

Isolating D:

D = 180 - 83 - 24.43

Subtracting numbers:

D = 72.57 ≈ 72.6 degrees