Find m∠V.
Understand the Problem
The question asks us to find the measure of angle V in a right triangle VWX. We are given the lengths of the two sides and the hypotenuse adjacent to angle V, so we can use trigonometric ratios (specifically cosine) to find the angle.
Answer
$m\angle V = 30^\circ$
Answer for screen readers
$m\angle V = 30^\circ$
Steps to Solve
- Identify the relevant trigonometric ratio
Since we have the adjacent side and the hypotenuse relative to angle $V$, we use the cosine function: $ \cos(V) = \frac{\text{adjacent}}{\text{hypotenuse}} $
- Substitute the given side lengths
$ \cos(V) = \frac{5\sqrt{78}}{10\sqrt{26}} $
- Simplify the fraction
$ \cos(V) = \frac{5}{10} \cdot \frac{\sqrt{78}}{\sqrt{26}} = \frac{1}{2} \cdot \sqrt{\frac{78}{26}} = \frac{1}{2} \cdot \sqrt{3} = \frac{\sqrt{3}}{2} $
- Find the angle V using the inverse cosine function
$ V = \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) $
- Determine the angle in degrees
$ V = 30^\circ $
$m\angle V = 30^\circ$
More Information
The angle $V$ is 30 degrees. This is a special right triangle (30-60-90 triangle).
Tips
A common mistake is using the incorrect trigonometric ratio (e.g., sine or tangent instead of cosine). Another mistake could be incorrectly simplifying the fraction before taking the inverse cosine.
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