Answer:
The best approximation for the measure of angle ABC is:
Third option: 58.3°
Step-by-step explanation:
This is a right triangle, because it has an angle of 90° (right angle) in vertex C, and we need one of the acute angles "x". We have the side opposite to the angle of 90° (right angle), this is the longest side in the right triangle, the Hypotenuse: H=20 cm
We have one of the legs (the sides form the right angle), and this leg is the Adjacent leg: A=10.5 cm to the angle "x".
To find the angle "x" we must use the trigonometric function that relates its adjacent leg (A) with the hypotenuse (H), and this function is cosine:
cos x = Adjacent Leg / Hypotenuse
cos x = A / H
Replacing the known values:
cos x = 10.5 cm / 20 cm
cos x = 0.525
Solving for x:
Rounding to 1 decimal place:
x=58.3°