Section 10.2: Non-right Triangles: Law of Cosines

What does the Law of Cosines relate in a triangle?

• The sum of the angles of a triangle to 180 degrees

• The square of any side of a triangle to the sum of the squares of the other two sides minus twice the product of these sides and the cosine of the included angle

• The area of the triangle to the square of its height

• The ratio of the lengths of sides opposite to their respective angles

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which formula is used to find the area of a triangle when all three sides are known?

• Heron's formula

• Pythagorean theorem

• Law of Sines

• Quadratic formula

Tags

CCSS.HSG.SRT.D.9

What is required to use the Law of Cosines to find a missing side in a triangle?

• All three angles

• Only one side and one angle

• Two angles and any side

• Two sides and the included angle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In the context of triangles, what does 'SAS' stand for?

• Side-All-Sides

• Segment-Angle-Segment

• Side-Angle-Side

• Sum-Angle-Sum

Tags

CCSS.HSG.SRT.B.5

What is the primary use of the Law of Cosines?

• To solve oblique triangles where a side and the two adjacent angles are known

• To calculate the height of geometric shapes

• To determine the radius of circumscribed circles

• To find the centroid of a triangle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How is the cosine of an angle calculated using the Law of Cosines when all sides of the triangle are known?

• (a^2 + c^2 - b^2) / (2ac)

• (b^2 + c^2 - a^2) / (2bc)

• (a^2 + b^2 - c^2) / (2ab)

• 2bc / (b^2 + c^2 - a^2)

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What does 'SSS' stand for in the context of solving triangles?

• Segment-Segment-Segment

• Side-Segment-Side

• Sum-Sum-Sum

• Side-Side-Side

Tags

CCSS.HSG.SRT.B.5

Which theorem is a special case of the Law of Cosines?

• Euler's Theorem

• Pythagorean Theorem

• Stewart's Theorem

• Theorem of Pappus

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the semi-perimeter in Heron's formula used for calculating the area of a triangle?

• Half of the triangle's perimeter

• Twice the area of the triangle

• The product of the triangle's sides

• The sum of the triangle's angles

Tags

CCSS.6.G.A.1

Which scenario is an example of when you would use the Law of Cosines?

• To find the length of a side in a triangle when two sides and the included angle are known

• To calculate the area of a square

• To determine the height of a parallelogram

• To find the diameter of a circle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11