Question

In right triangle ABC with the right angle at C, find angle A to the nearest tenth of a degree if a= 32.9 and c= 58.6? (DO NOT use the Law of Sines or Cosines.)

Answer 1

To find angle A in the right triangle, you can use the sine and cosine ratios. By substituting the given values into the equations, you can find the sine and cosine of angle A. Using the inverse sine function, you can then find the approximate value of angle A.

Step-by-step explanation:

To find angle A in the right triangle ABC, we can use the trigonometric ratios sine and cosine.

The sine of angle A is equal to the length of the side opposite angle A (a) divided by the length of the hypotenuse (c): sin(A) = a/c.

The cosine of angle A is equal to the length of the side adjacent to angle A (b) divided by the length of the hypotenuse (c): cos(A) = b/c.

Using the given values a = 32.9 and c = 58.6, we can substitute these values into the equations to find the values of sine and cosine of angle A.

sine(A) = 32.9 / 58.6 ≈ 0.561, cosine(A) = b / 58.6.

To find angle A, we can use the inverse sine function (sin⁻¹) with the approximate value of sine(A): A ≈ sin⁻¹(0.561) ≈ 33.9°.