Question

Solve the triangles with the given parts. 25) d = 5.60, € = 9.96, F = 109.1° Round to 4 decimal places as you work, then round your final answer to 1 decimal place.

Answer 1

We are given the following triangle:

We will determine the sides and angles of the triangle.

To determine the value o side f we will use the cosine law, which is the following:

`f^2=e^2+d^2-2(e)(d)cosF`

Now, we plug in the values:

`f^2=(9.96)^2+(5.6)^2-2(9.96)(5.6)cos(109.1)`

Solving the operations:

`f^2=203.7`

Now, we take the square root to both sides:

`\begin{gathered} f=√(203.7) \\ f=14.3 \end{gathered}`

Therefore, side "f" is 14.3.

Now, we will determine angle D using the sine law:

`(sinD)/(d)=(sinF)/(f)`

Now, we multiply both sides by "d":

`sinD=(sinF)/(f)d`

Now, we substitute the values:

`sinD=(sin(109.1))/(14.3)(5.6)`

Solving the operation:

`sinD=0.3`

Now, w take the inverse function of the sine:

`D=sin^(-1)(0.3)`

Solving the operations:

`D=17.2`

Therefore, angle D is 17.2°.

To determine angle E we will us the fact that the sum of the interiosr angles of a triangle adds p to 180:

`F+D+E=180`

Substitting the values:

`109.1+17.2+E=180`

Adding the values:

`126.3+E=180`

Now, we subtract 126.3 from both sides:

`\begin{gathered} E=180-126.3 \\ E=53.7 \end{gathered}`

Therefre, angle E is 53.7°