Question

Triangle UVW has a perimeter of 11.5 units. Solve for y.

Answer 1

Answer:

y = 3.2 units

Step-by-step explanation:

Find the missing angle measure x. Use the fact that all interior angle measures in a triangle add up to 180 degrees.

• 55 + 50 + x = 180
• 105 + x = 180
• x = 75

We can use the Law of Cosines to determine the missing side length y.

• a² = b² + c² - 2bc · cos(A)

Let's set UW (y) as a, WV as b, and UV as c. Therefore, ∠V must be A, ∠U must be B, and ∠W must be C.

Use the Law of Cosines to solve for a (side length y).

• a² = b² + c² - 2bc · cos(A)
• a² = (4)² + (3.5)² - 2(4)(3.5) · cos(50)
• a² = 28.25 - 28cos(50)
• a² =  28.25 - 17.99805307
• a² = 10.25194693
• a = 3.20186616366    

Side length y is equal to 3.2 units.