Question

In ΔXYZ, x = 5.9 meters, y = 8.9 meters, and z = 5.8 meters. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.

a) Solving Triangular Measurements
b) Triangle XYZ Dimensions
c) Geometric Calculations in ΔXYZ
d) Trigonometry in Triangle XYZ

Answer 1

To find the remaining measurements (angles) in triangle XYZ with sides x = 5.9m, y = 8.9m, and z = 5.8m, the Law of Cosines and Law of Sines can be applied. Assuming side x is opposite angle X, the Law of Cosines is used to solve for angle X, and then the Law of Sines or Law of Cosines for the remaining angles.

Step-by-step explanation:

The question pertains to solving for the remaining measurements of triangle XYZ where the lengths of the sides are given as x = 5.9 meters, y = 8.9 meters, and z = 5.8 meters. To find the remaining measurements such as the angles, we can use the Law of Cosines and Law of Sines. However, since the question does not specify which angle corresponds to which side, we'll assume x opposite angle X, y opposite angle Y, and z opposite angle Z for our calculations.

First, let's apply the Law of Cosines to find one angle, for instance angle X:

1. ² = y² + z² - 2yz cos(X)
2. cos(X) = (y² + z² - x²) / (2yz)
3. X = acos((y² + z² - x²) / (2yz))

Once angle X is calculated, we can use the Law of Sines to find the other angles, or continue with the Law of Cosines as needed.

After determining all angles, we would have all the Triangle XYZ Dimensions and can ensure the triangular measurements are complete by checking if the sum of all angles is approximately 180 degrees.