Okay for this question I know I am supposed to use the law of sines. But how can i tell what side is what?
In right triangle ABC, a = 120 and c = 140, and ÐC is the right angle. Solve the triangle. Round to the nearest tenth, if necessary.
angle A is opposite side a.
c/Sin90=a/SinA=b/SinB
of course! thanks!
To use the Law of Sines to solve a triangle, you need to know at least one angle and its corresponding side length. In this case, we have the right triangle ABC with angle C as the right angle and given side lengths a = 120 and c = 140.
First, let's label the sides of the triangle. The side opposite angle A is side a, the side opposite angle B is side b, and the hypotenuse, which is the side opposite the right angle C, is c.
Now, to determine which side is which, we can look at the given information. You mentioned that a = 120, which usually corresponds to the side opposite angle A. And c = 140 corresponds to the hypotenuse, which is the side opposite the right angle.
So, we have a = 120 and c = 140. By process of elimination, the remaining side, b, is the side opposite angle B.
Now that we know the sides, we can use the Law of Sines to find the missing angles and sides. The Law of Sines states:
sin(A) / a = sin(B) / b = sin(C) / c
In our case, we can use the formula sin(A) / a = sin(C) / c to find angle A:
sin(A) / 120 = sin(90°) / 140
To solve for sin(A), we can cross-multiply and then take the inverse sine of both sides:
sin(A) = (120 * sin(90°)) / 140
sin(A) ≈ 0.8571
Taking the inverse sine (sin^(-1)) of 0.8571, we find:
A ≈ 58.4°
Now that we know angle A, we can find angle B by using the fact that the sum of the angles in a triangle is 180°:
B = 180° - 90° - A
B ≈ 180° - 90° - 58.4°
B ≈ 31.6°
Lastly, to find the remaining side length b, we can use the Law of Sines again:
sin(B) / b = sin(C) / c
sin(31.6°) / b = sin(90°) / 140
To find b, we can cross-multiply and solve for it:
b ≈ (140 * sin(31.6°)) / sin(90°)
b ≈ 74.7
Therefore, in the right triangle ABC, side a is 120, side b is approximately 74.7, and side c is 140. Angle A is approximately 58.4°, angle B is approximately 31.6°, and angle C is 90°.