In ΔTUV, *t* = 920 inches, *u* = 480 inches and *v*=870 inches. Find the measure of ∠V *to the nearest degree.*

To find the measure of \(\angle V\) in \(\Delta TUV\), we can use the **Cosine Rule**. The Cosine Rule states:

\[
\cos V = \frac{t^2 + u^2 - v^2}{2tu}
\]

Given:

- \(t = 920\) inches (side opposite \(\angle T\))
- \(u = 480\) inches (side opposite \(\angle U\))
- \(v = 870\) inches (side opposite \(\angle V\))

Substituting the values into the formula:

\[
\cos V = \frac{920^2 + 480^2 - 870^2}{2 \times 920 \times 480}
\]

Now let's calculate it step by step:

\[
\cos V = \frac{(846400) + (230400) - (756900)}{2 \times 920 \times 480}
\]
\[
\cos V = \frac{319900}{883200}
\]
\[
\cos V \approx 0.3622
\]

To find the angle \(V\), take the arccosine:

\[
V = \cos^{-1}(0.3622) \approx 68^\circ
\]

So, the measure of \(\angle V\) is approximately **68°**.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How do you calculate the area of \(\Delta TUV\) using the side lengths?
2. What are the measures of the other angles \(\angle T\) and \(\angle U\)?
3. How do you verify the sum of angles in a triangle using the calculated values?
4. How would you find the length of the altitude from \(V\) to side \(tu\)?
5. What is the relationship between the sides of \(\Delta TUV\) in terms of inequalities?

**Tip:** When working with large numbers in trigonometric calculations, it's crucial to maintain precision throughout the steps to avoid rounding errors!

Learn how to find the measure of angle V in triangle TUV using the Cosine Rule with detailed steps and calculations. Given side lengths t = 920 inches, u = 480 inches, and v = 870 inches. Step-by-step solution provided with the arccosine function. Suitable for high school students.

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