Mathematics Law Sines-Cosines

What is the law of sine?

• The ratio of sides of a triangle and their respective cosine angles are equivalent to each other.

• The ratio of sides of a triangle and their respective secant angles are equivalent to each other.

• The ratio of sides of a triangle and their respective tangent angles are equivalent to each other.

• The ratio of sides of a triangle and their respective sine angles are equivalent to each other.

Answer explanation

The ratio of sides of a triangle and their respective sine angles are equivalent to each other.

What type of triangle does not contain any right angle?

• Equilateral Triangle

• Obtuse Triangle

• Isosceles Triangle

• Acute Triangle

Answer explanation

An Obtuse Triangle does not contain any right angle as it has one angle greater than 90 degrees. The other options may contain right angles or have specific angle properties.

In solving an oblique triangle, which two laws can be applied?

• Law of Tangents and Law of Secants

• Law of Sine and Law of Cosine

• Law of Cosine and Law of Cotangent

• Law of Cosecant and Law of Secant

Answer explanation

In solving an oblique triangle, the two laws that can be applied are the Law of Sine and Law of Cosine.

What does the Law of Sine formula represent?

• The ratio of sides of a triangle to the sines of their opposite angles.

• The ratio of sides of a triangle to the cosines of their opposite angles.

• The ratio of sides of a triangle to the cotangents of their opposite angles.

• The ratio of sides of a triangle to the tangents of their opposite angles.

Answer explanation

The Law of Sine formula represents the ratio of sides of a triangle to the sines of their opposite angles.

Which case in the Law of Sine involves two angles and a side opposite one of them?

• ASA Case

• SAS Case

• SSS Case

• AAS Case

Answer explanation

The ASA Case in the Law of Sine involves two angles and a side opposite one of them, making it the correct choice for this scenario.

What is the Law of Cosine formula for side c in a triangle?

• cos A = (b^2 + c^2 - a^2) / 2bc

• c^2 = a^2 + b^2 - 2ab(cos C)

• b^2 = a^2 + c^2 - 2ac(cos B)

• a^2 = b^2 + c^2 - 2bc(cos A)

Answer explanation

The Law of Cosine formula for side c in a triangle is c^2 = a^2 + b^2 - 2ab(cos C). This formula calculates the length of side c based on the lengths of sides a, b, and the angle C between sides a and b.

In triangle ABC with ∠C = 80°, a = 8, b = 12, what is the value of side c?

• 10.5

• 13.22

• 18.4

• 15.8

Answer explanation

Using the Law of Cosines, c = sqrt(a^2 + b^2 - 2ab*cos(C)) = sqrt(8^2 + 12^2 - 2*8*12*cos(80°)) = 13.22

If ∠A = 36.58° in triangle ABC with a = 8, b = 12, c = 13.22, what is the value of ∠B?

• 72.9°

• 63.42°

• 45.3°

• 27.6°

Answer explanation

Using the Law of Cosines, we can find ∠B = 63.42° by calculating cos(B) = (b^2 + c^2 - a^2) / (2bc) and then finding the arccosine of that value.

What is the Law of Cosine formula for angle A in a triangle?

• a^2 = b^2 + c^2 - 2bc(cos A)

• cos C = (a^2 + b^2 - c^2) / 2ab

• cos B = (a^2 + c^2 - b^2) / 2ac

• cos A = (b^2 + c^2 - a^2) / 2bc

Answer explanation

The Law of Cosine formula for angle A in a triangle is cos A = (b^2 + c^2 - a^2) / 2bc.

In triangle ABC with a = 15, b = 10, c = 20, what is the value of ∠A?

• 57.2°

• 69.4°

• 45.8°

• 32.7°

Answer explanation

In triangle ABC, using the Law of Cosines, we can find that ∠A is approximately 32.7° by using the formula cos(A) = (b^2 + c^2 - a^2) / (2bc).