# math

posted by .

I have spent hours trying to do these, help!

Use the given information to solve the triangle.

1) C = 145 degrees, b = 4, c = 14.

2) A = 150 degrees, C = 20 degrees, a = 200.

• math -

1)

Law of cosines:

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

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

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

C = 145°, c = 14, b = 4

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

14 ^ 2 = a ^ 2 + 4 ^ 2 - 2 a *4 *cos (C )

196 = a ^ 2 + 16 - 8 a *cos ( 145° )

196 - 16 = a ^ 2 - 8 a * cos ( 145° )

180 = a ^ 2 - 8 a * cos( 145° )

a ^ 2 - 8 a * cos( 145° ) - 180 = 0

cos ( 145 ° ) = - cos ( 35° ) = -0.81915

a ^ 2 - 8 a * ( -0.81915 ) - 180 = 0

a ^ 2 + 6,5532 a - 180 = 0

The solutions of this quadratic equation are :

a = - 17.0873

and

a = 10.5341

Length can't be negative so:

a = 10.5341

Law of Sines:

sin ( A ) / a = sin ( B ) / b = sin ( C ) / c

sin ( A ) / a = sin ( C ) / c Multiply both sides with a

sin ( A ) = a * sin ( C ) / c

sin ( A ) = 10.5341 * sin ( 145° ) / 14

sin ( 145° ) = sin ( 35° ) = 0.57357

sin ( A ) = 10.5341 * 0.57357 / 14

sin ( A ) = 6,042043737 / 14

sin ( A ) = 0,43157

A = 25° 34´

sin ( B ) / b = sin ( C ) / c Multiply both sides with b

sin ( B ) = b * sin ( C ) / c

sin ( B ) = 4 * 0.57357 / 14

sin ( B ) = 2.29428 / 14

sin ( B ) = 0.16388

B = 9 ° 26´

2)

B = 180° - 150° - 20 °

B = 10°

Law of Sines:

sin ( A ) / a = sin ( B ) / b = sin ( C ) / c

sin ( A ) / a = sin ( B ) / b Multiply both sides with b

b * sin ( A ) / a = sin ( B ) Divide both sides with sin ( A )

b / a = sin ( B ) / sin ( A ) Multiply both sides with a

b = a * sin ( B ) / sin ( A )

b = 200 * sin ( 10° ) / sin ( 150° )

sin ( 10° ) = 0.17365

sin ( 150° ) = sin ( 30°) = 0.5

b = 200 * sin ( 10° ) / sin ( 150° )

b = 200 * 0.17365 / 0.5

b = 34.73 / 0.5 = 34.73 * 2 = 69.46

Remark: 1 / 0.5 = 2

sin ( A ) / a = sin ( C ) / c Multiply both sides with c

c * sin ( A ) / a = sin ( C ) Divide both sides with sin ( A )

c / a = sin ( C ) / sin ( A ) Multiply both sides with a

c = a * sin ( C ) / sin ( A )

c = 200 * sin ( 20° ) / sin ( 150° )

sin ( 20° ) = 0.34202

c = 200 * sin ( 20° ) / sin ( 150° )

c = 200 * 0.34202 / 0.5

c = 68.404 / 0.5 = 68.404 * 2 = 136.808

## Similar Questions

1. ### Math

1. Find the value of Sin^-1(-1/2) a. -30 degrees b. 30 degrees c. 150 degrees d. 330 degrees 2. Find the exact value of cos(-420 degrees) a. -1/2 b. 1/2 c. sqrt of 3/2 d. -sqrt of 3/2 3. p(-9/41, 40/41) is located on the unit circle. …
2. ### Math

use the given information to solve the triangle. C= 85 degrees 20' a = 35 c = 50 I know that I have to find A,B,b but I do not know how to do this.

use the given information to solve the triangle. C= 85 degrees 20' a = 35 c = 50 I know that I have to find A,B,b but I do not know how to do this.
4. ### Math

Use the given information to solve the triangle. If two solutions exists, find both. A=110 degrees a=125 b=100 a is greater than b so I think that there is only one triangle. I am not sure where to go from here.
5. ### Math

Use the given information to solve the triangle. If two solutions exists, find both. A=110 degrees a=125 b=100 a is greater than b so I think that there is only one triangle. I am not sure where to go from here.
6. ### Math

Use the given information to solve the triangle. If two solutions exists, find both. A=110 degrees a=125 b=100 a is greater than b so I think that there is only one triangle. I am not sure where to go from here.
7. ### trigonometry

Use the given information to solve the triangle. 1) C = 145 degrees, b = 4, c = 14. 2) A = 150 degrees, C = 20 degrees, a = 200.
8. ### Math

Find the approximate number of radians, to the nearest hundreth, in the angles with the following dergree measures. a) 60 degrees b) 128.5 degrees c) 150 degrees d) 80 degrees e) 145 degrees f) 325 degrees g) 56.4 degrees h) 230 degrees …