The lengths of the hypotenuse and one leg of a righ triangle are 10.5 and 3.7 , respectively. Find the meas of the angle opposite the leg whose length is known.

To find the angle opposite the leg of length 3.7 in a right triangle with a hypotenuse of 10.5, you can use the sine function. The sine of an angle is the length of the opposite side divided by the hypotenuse. Here, \( \sin(A) = \frac{3.7}{10.5} \), which allows you to find the angle \( A \) by taking the inverse sine: \( A = \arcsin\left(\frac{3.7}{10.5}\right) \). Doing the calculations, you'll find that \( A \) is approximately \( 20.00^\circ \). And there you go! With some basic trigonometry, you've unveiled the angle hiding across from that 3.7 leg. It’s like revealing a secret about your triangle’s personality! You can use this knowledge in fields like architecture or engineering, where understanding angles is key to creating strong and stable structures!