In a right triangle, one leg measures $7$ units and the other leg measures $12$ units. Find the measure of the angle opposite the side of length $7$ to the nearest degree.

• A. $60°$
• B. $30.3°$
• C. $30°$
• D. $35°$

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle: the two legs are 7 units and 12 units, and the right angle is between these legs.
2. Recall that the angle opposite the side of length 7 units can be found using a trigonometric ratio involving the legs. Since we know the lengths of the two legs, use the tangent function, which relates the opposite side to the adjacent side: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).
3. Set up the equation for the angle \(\theta\) opposite the side of length 7 units: \(\tan(\theta) = \frac{7}{12}\).
4. To find the angle \(\theta\), take the inverse tangent (arctangent) of both sides: \(\theta = \tan^{-1}\left(\frac{7}{12}\right)\).
5. Use a calculator to evaluate \(\tan^{-1}\left(\frac{7}{12}\right)\) and round the result to the nearest degree to find the measure of the angle opposite the side of length 7 units.