Non-right Triangles & Trigonometry

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Question 1

Which of the following statements about the Law of Sines is correct?


  • It relates the angles of a triangle to the squares of the opposite sides.

  • It is only applicable in right triangles.

  • It relates the lengths of the sides of a triangle to the sines of their opposite angles.

  • It states that the sum of the sides of a triangle is equal to the product of the sides times the sine of one of the angles.

Question 2

What does the Law of Cosines calculate directly?

  • The area of a triangle

  • The cosine of an angle given all sides of the triangle

  • The length of a side given two sides and the included angle

  • The height of a triangle

Question 3

In triangle ABC, if angle A is 45 degrees, angle B is 55 degrees, and side a (opposite angle A) is 8 cm, how long is side b (opposite angle B)?

  • 8.76 cm

  • 9.25 cm

  • 7.89 cm

  • 6.53 cm

Question 4

Which of the following is a possible use of the Law of Sines?

  • To find an unknown angle given all three side lengths

  • To calculate the area of a triangle

  • To determine an unknown side when given two angles and one side

  • To verify if three points form a right triangle

Question 5

If in a triangle ABC, the sides are ( a = 7 ), ( b = 9 ), and ( c = 10 ), what is the measure of angle C using the Law of Cosines?

  • 53.13 degrees

  • 59.04 degrees

  • 67.38 degrees

  • 72.54 degrees

There are 5 questions to complete.

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