A triangle with sides 11 cm and 16 cm, and an angle of 74 degrees opposite x, is solved using the cosine rule. The calculated value for x is approximately 16.7 cm.
A) Completing the calculation:
Given a triangle with sides of 11 cm and 16 cm, and an angle of 74 degrees opposite the side of length x, we can use the cosine rule to find x.
B) Solving for x:
Substituting the given values into the cosine rule formula, we get:
x² = 11² + 16² - 2 × 11 × 16 × cos(74)
x² = 121 + 256 - 352 × cos(74)
x² = 377 - 352 × cos(74)
cos(74) ≈ 0.276
By substituting the value of cos(74) we can find the value of x.
x² = 377 - 352 × 0.276
x² = 377 - 97.15 cm
x² = 279.85
x ≈ 16.7
Therefore, the value of x is approximately 16.7 cm.
Hence, Given a triangle with sides 11 cm and 16 cm, and an angle of 74 degrees opposite side x, applying the cosine rule yields x ≈ 16.7 cm.