Questions: The diagram shows a triangle. What is the value of u? u= 0

Transcript text: The diagram shows a triangle. What is the value of $u$ ? \[ u= \] $\square$ 0 Submit

Solution

Solution Steps

Step 1: Identify the given information

The triangle has sides labeled $15u$ and $17u$ with an included angle of $116^\circ$.

Step 2: Use the Law of Cosines

The Law of Cosines states: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \] Here, $a = 15u$, $b = 17u$, and $C = 116^\circ$.

Step 3: Substitute the values into the Law of Cosines

\[ c^2 = (15u)^2 + (17u)^2 - 2 \cdot (15u) \cdot (17u) \cdot \cos(116^\circ) \]

Step 4: Simplify the equation

\[ c^2 = 225u^2 + 289u^2 - 2 \cdot 15u \cdot 17u \cdot \cos(116^\circ) \] \[ c^2 = 514u^2 - 510u^2 \cdot \cos(116^\circ) \]

Step 5: Calculate $\cos(116^\circ)$

Using a calculator: \[ \cos(116^\circ) \approx -0.4384 \]

Step 6: Substitute $\cos(116^\circ)$ back into the equation

\[ c^2 = 514u^2 - 510u^2 \cdot (-0.4384) \] \[ c^2 = 514u^2 + 223.584u^2 \] \[ c^2 = 737.584u^2 \]

Step 7: Solve for $u$

Since $c$ is not given, we need to find $u$ such that the equation holds true. However, without additional information about the third side or another angle, we cannot solve for $u$ directly from this equation alone.

Final Answer

The problem does not provide enough information to solve for $u$ directly. Additional information about the third side or another angle is required.

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