Question

solving triangles

Answer 1

A = 46, a=31, b=27

Answer 2

Since you are given 3 sides and no angles, you need to use the law of cosines to find one angle. Then use the law of sines to find another angle. Then use the sum of the measures of the angles to find the third angle.

Answer 3

i dont have three sides -.- i have 1 angle and 2 sides

Answer 4

Sorry. My mistake.
It's easier then.

Answer 5

Use the law of sines to find the angle opposite the given side of 27.
The use the sum of the measures of the angles to find the third angle.
Then use the law of sines again to find the third side.

Answer 6

sin46/31= sin?/27
then what?

Answer 7

By labeling the sides and angles we can avoid "sin?" and avoid confusion.

Answer 8

\(\dfrac{\sin 46^o}{31} = \dfrac{\sin B}{27}\)

Now you solve for B.
First solve the proportion for "sin B" by cross multiplying.
In other words, treat "sin B" as the unknown and solve for it.

Answer 9

i got 19.422 and i have 31x then what?

Answer 10

This is correct.
\(31 \sin B = 19.422\)

Now divide both sides by 31 to find sin B.

Answer 11

i just get .6265 etc.... but thats not one of my answers :c

Answer 12

Excellent.
Good work so far. Only one more step to find B.
We now know that
\(\sin B = 0.6265...\)

This is when you use the arcsine or the inverse sine function.
Instead of trying to find the sine of an angle, we are doing it in reverse.
We know the sine of an angle is 0.6265...
What is the angle.

We use the inverse sine function for that purtpose.

\(B = \sin^{-1} 0.6265\)

Answer 13

Use the inverse sine function of your calculator.

Answer 14

i got 38.8..... but how do i determine little c

Answer 15

That's what I got.
Good.

Answer 16

Now you know two angles, you can find the third angle with the sum of angles.

Answer 17

This will give you C (big C).

Answer 18

Once you have big C, then you can use the law of sines again to find little c.

Answer 19

so big c is 95.2 and then what do i do @mathstudent55

Answer 20

Now use the law if sines again to find little c.

Answer 21

is little c 25.7?

Answer 22

i also need help with one more question :c

Answer 23

\(\dfrac{\sin 46^o}{31} = \dfrac{\sin 95.2}{c}\)

\(c = 42.9\)

Answer 24

couldnt i just do a^2 + b^2=c^2
so 10^+7^2=c^2
so 149=c^2 and then what do i have to do?

Answer 25

Here you don't have the length of a side and the measure of its opposite angle for any side and opposite angle, so you must use the law of cosines.

Answer 26

a^2 + b^2 = c^2 is the Pythagorean theorem which only works for right triangles.
We don't know that this triangle is a right angle, so we can't use it.

Answer 27

oh :c so then what do i do?

Answer 28

What I wrote 2 answers ago.

Answer 29

i know.... but i dont know how to do that

Answer 30

First, we need to label all your sides and angles. Can you please copy your figure, and label every side and angle?

Answer 31

I mean with a, b, c, A, B, C.

Answer 32

i know what you mean c:

Answer 33

Great.
The law of cosines can be written three different ways. We pick the way that helps us.

\(a^2 = b^2 + c^2 - 2bc \cos A\)

\(b^2 = a^2 + c^2 - 2ac \cos B\)

\(c^2 = a^2 + b^2 - 2ab \cos C\)

Answer 34

.-. so 149-2(10)(7) cos52?

Answer 35

and i got 62.8

Answer 36

which equals 7.9

Answer 37

\(a^2 = 10^2 + 7^2 - 2(10)(7) \cos 52^o\)

\(a^2 = 149 - 140 \cos 52^o\)

\(a^2 = 62.8\)

\(a = 7.9\)

You are correct.

Answer 38

okay thank you c:

Answer 39

Do you need any more parts of this triangle?