Mastering Oblique Triangles

What is the Law of Sines?

• The Law of Sines states that all angles in a triangle are equal.

• The Law of Sines relates the sides of a triangle to the sines of its angles.

• The Law of Sines is used to calculate the area of a triangle.

• The Law of Sines applies only to right triangles.

Given triangle ABC, if angle A = 30° and side a = 10, find side b if angle B = 45°.

• 10

• 5√2

• 15

• 10√2

In triangle XYZ, if angle X = 60° and side x = 12, find angle Y if side y = 10.

• 41.81°

• 30°

• 50°

• 75°

How do you apply the Law of Sines to find a missing angle?

• Use the Law of Sines to rearrange and solve for the missing angle.

• Use the Pythagorean theorem to find the angle.

• Multiply the sides of the triangle to find the angle.

• Subtract the known angles from 180 degrees.

If angle A = 50° and side a = 8, and side b = 10, what is angle B?

• 60°

• 50.1°

• 45°

• 70°

In triangle DEF, if angle D = 70° and side d = 15, find side e if angle E = 40°.

• 10.25

• 8.50

• 12.75

• 9.14

What is the relationship between the angles and sides in the Law of Sines?

• The Law of Sines states that the angles of a triangle are equal to the lengths of the sides.

• The Law of Sines only applies to right triangles and does not involve angles.

• The Law of Sines relates the ratios of the lengths of the sides of a triangle to the sines of the angles opposite those sides.

• The Law of Sines relates the sum of the angles in a triangle to the product of the sides.

If angle C = 90° in triangle GHI, how can you find angle G if side g = 5 and side h = 7?

• G = arcsin(5/7)

• G = 90° - arctan(5/7)

• G = 180° - arccos(5/7)

• G = arccos(5/7)

Given triangle JKL with angle J = 45° and side j = 5, find angle K if side k = 8.

• 53.13°

• 60°

• 45°

• 30°

How can you determine if a triangle is solvable using the Law of Sines?

• A triangle is solvable if you have AAS, ASA, or SSA conditions.

• A triangle is solvable if all sides are known.

• A triangle is solvable if it has three equal sides.

• A triangle is solvable only if it has a right angle.