Question

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. Statements: x² + 3² = 6², where x is the 3rd side of the triangle. x² = 3² +6² + 2⋅3⋅6⋅cos 60°, where x is the 3rd side of the triangle. x² = 3² + 6² − 2⋅3⋅6⋅cos60°, where x is the 3rd side of the triangle. (sin 60°)/3 = (sinθ)/6, where θ is an unknown angle.

Answer 1

c² = 3² +6² - 2⋅3⋅6⋅cos 60

c = 27ft

Explanation:

Since the angle is located in between the sides of the sides, we will use the cosine rule to get the unknown sides

Let c be the missing sides

According to the cosine rule;

c² = a²+ b² - 2abcosC

c² = 3² +6² - 2⋅3⋅6⋅cos 60

c² = 9 + 36 - 36cos60

c² = 45 - 36cos60

c² = 45 - 36(0.5)

c² = 45 - 18

c² = 27ft

Hence the missing attribute is 27ft and the required expression is c² = 3² +6² - 2⋅3⋅6⋅cos 60