👑Q Trig: Law of Sine review

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, use the 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 angle B = 45°, how do you find angle C?

Back

Use the triangle sum theorem: C = 180° - A - B. So, C = 180° - 30° - 45° = 105°.

Front

What is the relationship between the 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 do you calculate the area of a triangle using the Law of Sines?

Back

Area = (1/2) * a * b * sin(C), where a and b are two sides of the triangle and C is the included angle.

Front

What is the angle of depression?

Back

The angle of depression is the angle formed by a horizontal line and the line of sight to an object below the horizontal line.

Front

How do you find the distance to an object using angles of depression?

Back

Use trigonometric ratios, such as tangent, to relate the height of the object and the distance from the observer.

Front

If Tia and Braden are 12 feet apart and the angles of depression to the goggles are 65° and 28°, how do you find the distance from Tia to the goggles?

Back

Use the Law of Sines or trigonometric ratios to set up equations based on the angles and the distance between Tia and Braden.

Front

What is the sine of an angle?

Back

The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.