Two sides of a triangle have measures 3 ft and 6 ft. Also, these sides form a vertex whose angle measures 60 degrees. Calculate the missing attributes of the triangle.

A. The length of the third side is approximately 5 feet.

B. A = , B = and C = .

Step-by-step explanation:

Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.

A. Let side a = 6 feet and c = 3 feet, thus;

= + - 2ac Cos B

  = + - 2(6 x 3) Cos

  = 36 + 9 - 36 x 0.5

  = 45 - 18

= 27

b =

  = 5.1962

b  = 5.2 feet

b ≅ 5 feet

The length of the third side is approximately 5 feet.

B. Given that B = , then let us apply the Sine rule to determined the measure of A.

=

So that,

=

Sin A =

Sin A = 0.99923

A = 0.99923

  = 87.75

A ≅

Since the sum of angle in a triangle = .

Then,

A + B + C =

+ + C =

+ C =

C = -

     =

C =

Thus,

A = , B = and C = .