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:

$\begin{gathered} f=\sqrt{203.7} \\ f=14.3 \end{gathered}$

Therefore, side "f" is 14.3.

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

$\frac{sinD}{d}=\frac{sinF}{f}$

Now, we multiply both sides by "d":

$sinD=\frac{sinF}{f}d$

Now, we substitute the values:

$sinD=\frac{sin(109.1)}{14.3}(5.6)$

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°