Construct a triangle xyz such that xy=7cm yz=10cm yxz=105:measure xz
see above
construct the angle.
Label X,Y,Z
measure XZ
To see whether you have done it right, use the law of cosines to calculate XZ.
To find the measurement of line segment XZ in triangle XYZ, we can use the Law of Cosines. This formula allows us to calculate the length of one side of a triangle if we know the lengths of the other two sides and the measure of the included angle.
The Law of Cosines states: c^2 = a^2 + b^2 - 2ab * cos(C), where c represents the side opposite to angle C and a and b represent the other two sides of the triangle.
In our case, XY is 7 cm, YZ is 10 cm, and angle XYZ is 105°. We want to find the measurement of XZ.
Let's apply the Law of Cosines to find XZ:
XZ^2 = XY^2 + YZ^2 - 2 * XY * YZ * cos(angle XYZ)
XZ^2 = 7^2 + 10^2 - 2 * 7 * 10 * cos(105°)
XZ^2 = 49 + 100 - 140 * cos(105°)
Now, we need to calculate cos(105°):
cos(105°) = cos(180° - 105°)
cos(105°) = cos(75°)
To calculate cos(75°), we can use the unit circle or a calculator:
cos(75°) ≈ 0.2588
Now, substitute this value back into our equation:
XZ^2 = 49 + 100 - 140 * 0.2588
XZ^2 = 49 + 100 - 36.232
XZ^2 ≈ 112.768
Finally, take the square root of both sides to find XZ:
XZ ≈ √112.768
XZ ≈ 10.627 cm
Therefore, the measurement of line segment XZ in triangle XYZ is approximately 10.627 cm.