Please help with trig problem?

Question

In the following exercise, solve the triangle.
b = 17.1, c = 29.3, B = 27.6°

A =__ ° (larger value for A)
C =__ °
a =__

A =__° (smaller value for A)
C =__ °
a =__

Answer 1

C=52.55 ....................sine rule
A=99.85 ....................sum of angles = 180
a=36.37 ....................cos or sin rule
or
C=180 - 52.55=127.45
A= 24.95 ...................sum of angles = 180
a=41.95 ....................cos or sin rule

the end

Answer 2

At firast you can yuse the cos-formula:
(^ = Power & * = multiplication)

b^2 = c^2 + a^2 - 2*a*c+ cos (B)
17.1^2 = 29.3^2 + a^2 - 2*a*29.3*cos (27.6). By using your calculator you get the following equation.

a^2 - 51.93*a -17.1^2 + 29.3^2 = 0
a^2 - 51.93*a + 566,08 = 0

By solving this equation >> a1 = 36.36 and a2 = 15.52 ( the slight deviation by calculating is due to after-dot reduction/correction!)

Here you use the sine-formula:

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

1) 36.36/sin(A) = 17.1/sin(27.6) = 29,3/sin(C)36.909 >>>
sin(A) = 0.985 and sin(C) = 0.794 >> you get for both A and C zwo angles. You should be absolutely careful because the sum of the angles must be at any rate equal to 180. You have definitely B = 27.6 >>
then: A + C = 152.4.
If you solve sin(A) = 0.985 for the smaller angle, you will get A = 80 and consequently C = 72.4. but sin(72.4) = 0.953. We have a false result, because we hat got it previously sin(C) = 0.794 !!

If you solve sin(A) = 0.985 for the greater angle, the you get A = 100 and C = 152.4 -100 = 52.4, which fulfill the equation sin(C) = 0.794.

Therefor : A = 100; C = 52.4 and a1 = 36.36
Please check this calculation in detail.

For a2 = 15.52 you can solve this problem with the same procedure. But take always into consideration the restrictions in a triangle.

Answer 3

what 'chu think you should use when you see this problem?

hm... law of sines =)

you know, from your trig class that...

(a/sinA) = (b/sinB) = (c/sinC)

let's use the values given =)

Find angle C -- (17.1)/(sin27.6) = (29.3)/(sinC)
sinC = ((29.3)(sin27.6))/(17.1)
*take the inverse sin of ((29.3)(sin27.6))/(17.1)
*in order to find that angle.
C = 52.5*

Find angle A -- angle A = 180 - angle B + angle C
*all angles add up to 180* in a triangle right?
angle A = 180 - 27.6* + 52.5*
angle A = 99.9*

Find length a -- a/(sin99.9*) = (17.1)/(sin27.6)
a = ((17.1)/(sin27.6))/(sin27.6)
a = 36.4

you should be able to find rest =)

Answer 4

sinC = (29.3/17.1)sin(27.6°)
sinC = 0.7938347
C ≈ 52.545°, 127.455°
A ≈ 99.855°, 24.945°
a = 36.365, 15.566

Answer 5

Using Sinus formula:
c/sin C =b/sin B
sin C
=cx(sin B)/b
=(29.3)x(sin 27.6 deg)/17.1
=0.793835

C=arcsin 0.793835
=52.5 or 127.5 deg

A=180 deg - 52.5 deg - 27.6 deg =99.9 deg (large value)
or
A=180 deg - 127.5 deg -27.6 deg =24.9 deg (small value)

Using Cosinus formula:
a=surd(b^2 +c^2 -2bc cos A)
=surd((17.1)^2 + (29.3)^2 -2(17.1)(29.3)cos 99.9)
=surd(1322.4022)=36.4
or
a=surd(b^2 +c^2 -2bc cos A)
=surd((17.1)^2 + (29.3)^2 -2(17.1)(29.3)cos 24.9)
=surd(242.3216)=15.6

SUMMARY:
A=99.9 deg (large value)
C=52.5 deg
a=36.4

A=24.9 deg (small value)
C=127.5 deg
a=15.6