Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
B = 29°, b = 26, c = 28

A = 92.5°, C = 58.5°, a = 12.6; A = 87.5°, C = 121.5°, a = 12.6

A = 119.5°, C = 31.5°, a = 14.5; A = 2.5°, C = 148.5°, a = 14.5

A = 92.5°, C = 58.5°, a = 53.6; A = 87.5°, C = 121.5°, a = 53.6

A = 119.5°, C = 31.5°, a = 46.7; A = 2.5°, C = 148.5°, a = 2.3

Answer 1

\[(\sin A)/a = (\sin B)/b=(\sin C)/c\]

Answer 2

im just starting this...can you explain please

Answer 3

using the Law of SInes we can write this:
\[\Large \frac{b}{{\sin \beta }} = \frac{c}{{\sin \gamma }} \Rightarrow \frac{{26}}{{\sin 29}} = \frac{{28}}{{\sin \gamma }}\]

Answer 4

All triangles follow the Sine Law. Which is to say that the ratio of an angle and the side with which the angle isn't connected with (the opposite side) is equal to ratio of an angle and its opposite side.
Hence (sinA)/a=(sinB)/b=(sinC)/c
Plug the values of variables into their corresponding positions and you will work out the values of the unkwown variables.

Answer 5

therefore we have:
\[\Large \sin \gamma = \frac{{28}}{{26}} \cdot \sin 29 = ...?\]

Answer 6

31.2

Answer 7

I got a different result:
\(\Large \gamma \simeq 31.5\) degrees

Answer 8

oh wait yeah. my mistake

Answer 9

now, since the sum of interior angles has to be equal to 180 degrees, we can write:
\[\Large \begin{gathered}
\alpha = 180 - \left( {\beta + \gamma } \right) = \hfill \\
\hfill \\
= 180 - \left( {29 + 31.5} \right) = ...? \hfill \\
\end{gathered} \]

Answer 10

119.5

Answer 11

correct!

Answer 12

finally, if we apply the Law of Sines again, we can write this:
\[\Large \frac{a}{{\sin 119.5}} = \frac{{26}}{{\sin 29}}\]

Answer 13

therefore:
\[\Large a = \sin \left( {119.5} \right) \cdot \frac{{26}}{{\sin 29}}=...?\]

Answer 14

107.14

Answer 15

hint:
we have this:
\[\Large \begin{gathered}
a = \sin \left( {119.5} \right) \cdot \frac{{26}}{{\sin 29}} = \hfill \\
\hfill \\
= 0.870 \cdot \frac{{26}}{{0.485}} = ...? \hfill \\
\end{gathered} \]

Answer 16

46.63

Answer 17

that's right!

Answer 18

would the answer be the last choice?

Answer 19

yes! It is: A = 119.5°, C = 31.5°, a = 46.7

Answer 20

b and d have a similar answer how do I tell which one is correct?

Answer 21

oh the a

Answer 22

Thank you so much!

Answer 23

it is the option of the fourth row, of the left column