Math Problem Statement

Determine the value of ∠V in the triangle with given sides and angle.

Solution

To determine the value of angle V\angle V in the given triangle, we can use the sine rule or the cosine rule, depending on the information provided. In this case, the triangle has one known angle and two sides. Here's how you can proceed:

The given information:

  • Angle T=31\angle T = 31^\circ
  • Side TU=11.1cmTU = 11.1 \, \text{cm}
  • Side TV=5.8cmTV = 5.8 \, \text{cm}

We can apply the sine rule, which states:

TVsin(V)=TUsin(T)\frac{TV}{\sin(\angle V)} = \frac{TU}{\sin(\angle T)}

Substitute the known values:

5.8sin(V)=11.1sin(31)\frac{5.8}{\sin(\angle V)} = \frac{11.1}{\sin(31^\circ)}

Now, solving for sin(V)\sin(\angle V):

sin(V)=5.8sin(31)11.1\sin(\angle V) = \frac{5.8 \cdot \sin(31^\circ)}{11.1}

Once you calculate the value of sin(V)\sin(\angle V), you can find V\angle V by taking the inverse sine (arcsin) of the result.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine Rule

Formulas

Sine Rule: \( \frac{a}{\sin(A)} = \frac{b}{\sin(B)} \)

Theorems

Sine Rule

Suitable Grade Level

Grades 9-11