Trigonometry - solving?

Question

Thank you to all those who answered my previous ques.!!! :)

Heres the last que. I was having a little bit trouble with:
Solve ----> a=25 b=11 c=24

So, this is what I did:

Cos B = a^2 + c^2 - b^2
---------------------
2 a c

= 25^2 + 11^2 - 24^2
---------------------------
2 x 25 x 24

= 170/1200

B = Cos^-1 (0.1416)
= 81.86 deg

The prob. comes here: ( I use the laws of sin )
b c
----- = -------
sin B sin C

11 24
---------- = -----------
sin 81.86 sin C

sin C = 2.16

But I can NOT put it into --------> Sin^-1 (2.16)
It gives an error.

So how can I find the degree of C?

Answer 1

I hate to tell you this, but you've got your Law of Cosines equation wrong in the first step. The Law of Cosines states that b^2=a^2=c^2-2(a)(c)(cos B).

Let's solve:
11^2=25^2+24^2-2(25)(24)(cos B)
121=625+576-1200(cos B)
1200(Cos B)=1080
cos B=.9
B=25.84 deg

11/sin 25.84 = 24/sin C
(11)(sin C)=(24)(sin 25.84)
sin C=.95
C=71.98 deg

11/sin 25.84=25/sin A
(11)(sin A)=(25)(sin 25.84)
sin A=.99
A=82.13 deg

I hope that helps!

Answer 2

Looking over your work I found a mistake in the first equation. In the given work you have a = 25, b = 11 and c=24. When you put it into the equation you have c = 11 and b = 24. When I recalculate the equation I get:

1080/1200 = 0.9

Try that and see if it makes your answer better.

Good Luck!!!

Answer 3

I would start by solving for angle A first, then angle B, then angle C. (use the law of cosines)
25^2 = 11^2+24^2-2(11)(24)cosA
A = 82.2
11^2 = 24^2+25^2-2(25)(24)cosB
B = 25.8
So then, C = 180-82.2-25.8 = 72
I think your setup is incorrect at the very beginning.

Answer 4

The textbook is incorrect. sin(2x) = a million permit's take a glance on the consumer-friendly sine values in quadrant I on the unit circle. sin(0°) = 0 sin(30°) = a million/2 sin(40 5°) = ?2/2 sin(60°) = ?3/2 sin(ninety°)= a million the only time that sin(?) = a million is at ninety°. sin(2x) = a million = sin(ninety°) 2x = ninety° x = 40 5° The 4 circumstances it particularly is equivalent on the unit circle are 40 5°, a hundred thirty five°, 225°, and 315°.

Answer 5

Half your problem is not using ( ) to keep your numerators and denominators from getting confused.

The other half is that your answer is wrong because you didn't substitute correctly into your law of cosine relation; (b) and (c) values were switched.

Answer 6

Where did you get that first equation? Its completely made up because you cant manipulate algebraic expressions properly.

Try this

a^2 + c^2 - b^2 = cos B
---------------------
2 a c

Answer 7

it's an error because sin can never be greater than 1 or less than -1

Answer 8

sin C not equal to 2.16

if u want to use sine law :

ab / sinC = ac /sinB
so,
sinC = (absinB )/(ac)
C =26.98=27 degree

Answer 9

try solving using radian mode