B = 68°24'36", C = 54°13'48", b = 12.57
Here is a little trick if your calculator has a key looking something like D°M'S
you can key in the traditional "degree-minute-second" notation directly and do arithmetic
e.g
to enter
B = 68°24'36"
press 68
D°M'S
24D°M'S
36
=
it should show: 68°24'36.00
change it to a standard decimal notation by pressing
2ndF and then D°M'S
I get B = 68.41° and C = 54.23°
ok then ...
we know angle A = 57.36°
Now we can find the other two sides using the sine law.
e.g. BC/sin57.36 = 12.57/sin68.41
BC = 12.57sin57.36/sin68.41
= 11.38
find AB in the same way
reiny am i dooing it right ??
AB = 12.57(sin 54.23)/sin 57.36
= 12.11
I don't think so,
AB/sinC = 12.57/sinB
AB = 12.57sin54.23/sin68.41
To find the remaining angles of the triangle, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant.
In this case, we have the following information:
- B = 68°24'36" (which can be converted to decimal degrees as 68.41°)
- C = 54°13'48" (which can be converted to decimal degrees as 54.23°)
- b = 12.57
We can use the Law of Sines to find the lengths of the other sides of the triangle. The formula is:
sin(A)/a = sin(B)/b = sin(C)/c
Now, let's find angle A first. We can rearrange the formula as:
sin(A) = (b * sin(C)) / c
Plugging in the values we have:
sin(A) = (12.57 * sin(54.23°)) / c
Now, we need to find the value of c. We can use the Law of Sines again:
sin(C)/c = sin(A)/a
Plugging in the values we have:
sin(54.23°) / c = sin(A) / 12.57
Now, we have two equations with two unknowns (A and c). We can solve these equations simultaneously to find the values.
Let's start by finding A:
sin(A) = (12.57 * sin(54.23°)) / c
A = arcsin((12.57 * sin(54.23°)) / c)
Now, let's find c:
sin(54.23°) / c = sin(A) / 12.57
c = (sin(A) * 12.57) / sin(54.23°)
By plugging in the value of A obtained from the previous equation, we can find c.
Once we have the values of A and c, we can find the remaining angle of the triangle, which is angle B.
Please note that the accuracy of the answer depends on the accuracy of the values provided.