+148 The hypotenuse of a right triangle measures 2 sq root 15 centimeters and its shorter leg measures 2 sq root 6 centimeters. What is the measure of the larger acute angle of the triangle? Round your answer to the nearest tenth of a degree.
+1253 Answer: 50.8 degrees
Explanation:
Obviously, by Pythagorean Theorem, the longer leg is 6.
Longer leg is opposite larger angle.
We can use law of cosines to get \(6^2=(2\sqrt{15})^2+(2\sqrt{6})^2-2 \times (2\sqrt{15})\times (2\sqrt6) \times \cos{\theta}\)
Simplifying, \(-48=-24\sqrt{10} \times \cos{\theta}\), so \(\frac{\sqrt{10}}{5}=\cos{\theta}\).
Assuming you can use a calculator, use inverse cosine function to get \(\theta \approx 50.7685 \circ\), and rounding to the nearest tenth, the angle is 50.8 degrees.
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