Question

In ΔTUV, v = 94 cm, t = 27 cm and ∠U=144°. Find the length of u, to the nearest centimeter.

Answer 1

The question involves using the Law of Cosines to find the length of side u in triangle TUV. By substituting the given values into the Law of Cosines formula, we can solve for u and round to the nearest centimeter.

Step-by-step explanation:

The student is asking to find the length of side u of triangle ΔTUV given the lengths of sides v and t, and the measure of angle ∠U. This is a problem of solving for the unknown side in an oblique triangle using the Law of Sines or Law of Cosines. Given that the angle ∠U is provided, we will use the Law of Cosines in this case.

Step-by-step explanation:

1. Identify the known sides and angle: v = 94 cm, t = 27 cm, and ∠U = 144°.
2. Apply the Law of Cosines formula: u² = t² + v² - 2 * t * v * cos(∠U).
3. Substitute the known values and calculate: u² = 27² + 94² - 2 * 27 * 94 * cos(144°).
4. Solve for u: Take the square root of the result from step 3 to find the length of u.
5. Round the result to the nearest centimeter.

Answer 2

x²=94²+27²-2(94)(27)cos(144)

x²=13671.57

x=117cm