In triangle ABC, side AB = 10, angle B = 65 degrees, and angle C = 45 degrees. What is the length of side BC?
You try this one, I gave you the solution for your other trig problem.
Hint:
you can find the third angle easily.
Then use the Sine Law.
To find the length of side BC in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the sine of an angle to the length of its opposite side is constant for all three angles in a triangle.
In this case, we have side AB and angle B given. Let's label side BC as "b", angle C as "C", and angle A as "A".
First, we need to find angle A. Since the sum of the angles in a triangle is 180 degrees:
angle A = 180 - angle B - angle C
angle A = 180 - 65 - 45
angle A = 70 degrees
Now, we can use the Law of Sines to find the length of side BC:
sin A / AB = sin C / BC
Substituting the known values, we get:
sin 70 / 10 = sin 45 / BC
Now, we can rearrange the equation to solve for BC:
BC = (10 * sin 45) / sin 70
Using a calculator, we can find that sin 45 is approximately 0.7071 and sin 70 is approximately 0.9397:
BC = (10 * 0.7071) / 0.9397
Simplifying further, we get:
BC ≈ 7.071 / 0.9397
BC ≈ 7.526
Therefore, the length of side BC is approximately 7.526.