Need help ASAP with law of sines and finding side b of triangle using law of sines please help

Question

Find the value of side b for each triangle using The Law of Sines: 

1)A=24.3 degrees C=54.6 degrees a=2.68

2)B=10 degrees C=135 degrees c=45

3)A=10 degrees B=60 degrees a=7.5

 

Answer 1

The law of sines for a triangle, in one form, is that:

 

(sin A)/a = (sin B)/b = (sin C)/c, where a, b, and c are the side lengths and A, B, and C are the corresponding angles opposite those sides.

 

2) and 3) can be solved directly with this.  For example, for 2)

 

(sin 135)/45 = (sin 10)/b

 

Cross-multiplying gives:  b(sin 135) = 45(sin 10) --> b = 45((sin 10)/sin(135)) ~ 45(0.246) = 11.05

 

3) can be solved in exactly the same way, just using (sin A)/a in place of (sin C)/c

 

For 1), we have to do a little extra work, because B is not given.  But, for a triangle, the sum pf interior angles must equal 180 degrees.  So 24.3 + 54.6 + B = 180, and B = 180 - 24.3 - 54.6 = 101.1 degrees.  Then, just follow the same procedure as above.

 

Hope this helps!

 

 

Answer 2

in the first case

first we need to find angle B

we use the fact that sum of angles in a triangles is 180

so B+24.3+54.6=180

B = 180 -  78.9= 101.1

now to sine law:

a/sinA= b/sinB

so b=a sinB/sin A

b= 2.68 sin(101.1)/sin (24.3)

use calculator to find result for questions  1

im using my phone unfortunately! 

for question 2 and 3 same methodology. in question you are given angle B so no need to look for it. just use law of sine immediately like this

b=c sinB/sinC

for 3 again you are given angle B

so using law of sine 

write b= a sinB/sinA= 7.5 sin60/sin10

best of luck!