Final answer:
Using the Law of Cosines with the given values for sides y and z and angle X, the length of side x is calculated to be approximately 7.0 cm to the nearest tenth of a centimeter.
Step-by-step explanation:
The student is asking for help in finding the length of side x in triangle XYZ, given that side y is 6.1 cm, side z is 7.5 cm, and angle X is 61°. This is a problem in trigonometry, specifically using the Law of Cosines. To find the length of side x, we use the formula x = √(y² + z² - 2yzcos(X)).
Let's apply the values:
x = √((6.1²) + (7.5²) - 2(6.1)(7.5)cos(61°))
x = √((37.21) + (56.25) - (91.5)cos(61°))
x = √(93.46 - 91.5(0.4848))
x = √(93.46 - 44.3874)
x = √(49.0726)
x ≈ 7.0 cm
The length of side x, to the nearest tenth of a centimeter, is approximately 7.0 cm.