Final answer:
To calculate the length of BC in triangle ABC with angles BAC = 95° and ABC = 34°, and side AB = 5 cm, we first find angle BCA. Sum of angles in a triangle is always 180°, which gives us BCA = 51°. Then, using the Law of Sines, we can find the length of side BC.
Step-by-step explanation:
To find the length of BC in triangle ABC, where AB = 5 cm, angle BAC = 95°, and angle ABC = 34°, we first recognize that we have a case of the Law of Sines, as we are dealing with two angles and a non-included side. However, in triangle ABC, we are missing angle BCA to apply the Law of Sines directly. Once we find angle BCA, we can use the Law of Sines to calculate the length of BC.
First, we determine angle BCA by using the fact that the sum of angles in a triangle is 180 degrees. Therefore, angle BCA = 180° - angle BAC - angle ABC = 180° - 95° - 34° = 51°.
Now that we have all three angles, we can use the Law of Sines:
- sin(A) / a = sin(B) / b = sin(C) / c
We rearrange the formula to solve for side BC (c):
c = a * sin(C) / sin(A)
Using the given values and substituting into the equation:
c = 5 cm * sin(51°) / sin(95°)
After calculating this expression using a scientific calculator, we get the length of BC.