Question

suppose you have a right triangle whose two short sides are of length 3 and 4 respectively. then the smaller of the two acute angles is degrees and the larger acute angle is degrees. if you enter your angles as decimal approximations compute at least one digit beyond the decimal point. hint: compute the length of the hypotenuse, use it to compute sines of the angles in question, and then apply the inverse sine function. set your calculator to degree mode. if you use the ww asin function make sure you convert to degrees.

Answer 1

The smaller acute angle is approximately 36.87 degrees and the larger acute angle is approximately 53.13 degrees.

Step-by-step explanation:

To find the smaller acute angle of the right triangle, we can use the sine function. The sine of an acute angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is 3 and the hypotenuse is √(3² + 4²) = 5. So, the sine of the smaller acute angle is sin(x) = 3/5. Taking the inverse sine of 3/5, we get x ≈ 36.87 degrees.

Similarly, to find the larger acute angle, we can use the cosine function. The cosine of an acute angle is equal to the ratio of the length of the adjacent side to the length of the hypotenuse.

In this case, the adjacent side is 4 and the hypotenuse is 5. So, the cosine of the larger acute angle is cos(y) = 4/5. Taking the inverse cosine of 4/5, we get y ≈ 53.13 degrees.