Question

Suppose a triangle has two sides of length 3 and 4 and that the angle between these two sides is 60°. What is the length of the third side of the triangle?


A) 3
B) Square root 13
C) 4 Square root 3
D) Square root 3

Answer 1

Answer:

sqrt(13)

B

Step-by-step explanation:

This problem uses the Cos law

Givens

• a = 3
• b = 4
• C = 60 degrees

Formula

c^2 = a^2 + b^2 - 2*a*b*Cos(C)

Solution

• c^2 = a^2 + b^2 - 2*a*b*Cos(C)     Substitute givens
• c^2 = 3^2 + 4^2 - 2*3*4*Cos(60)   Evaluate
• cos(60) = 1/2                                   Evaluate
• c^2 = 9 + 16 - 2* 3 * 4 * 1/2             Add the first two term. The third term is 12
• c^2 = 25 - 12                                   Subtract
• c^2 = 13                                           Take the square root of both sides.
• c = sqrt(13)                                       Answer

Answer 2

Answer:

B) Square root 13

Step-by-step explanation:

AP3X