HW: Dec 12 Law of Sines

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Front

How do you find a missing side using the Law of Sines?

Back

To find a missing side, rearrange the Law of Sines formula: a = (b * sin(A)) / sin(B), where A and B are the angles opposite sides a and b, respectively.

Front

What is the formula for the Law of Sines?

Back

The formula is: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

Front

If angle A = 30° and side a = 10, how do you find side b?

Back

Use the Law of Sines: b = (a * sin(B)) / sin(A). First, find angle B, then substitute the values.

Front

What is the relationship between angles and sides in a triangle?

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

How can the Law of Sines be used to find an angle?

Back

To find an angle, rearrange the Law of Sines: A = sin^(-1)(a * sin(B) / b).

Front

What is the significance of the sine function in the Law of Sines?

Back

The sine function relates the angles of a triangle to the ratios of the lengths of its sides, allowing for the calculation of unknown sides or angles.

Front

If angle B = 45° and side b = 14, how do you find side a if angle A = 30°?

Back

Use the Law of Sines: a = (b * sin(A)) / sin(B) = (14 * sin(30°)) / sin(45°).

Front

What is the sine of 30 degrees?

Back

The sine of 30 degrees is 0.5.

Front

What is the sine of 45 degrees?

Back

The sine of 45 degrees is approximately 0.707.