Answer:
0.28
Explanation:
In the given right triangle ΔABC, with right angle at C, we can use the cosine formula to find the value of cos(∠A):
cos(∠A) = adjacent/hypotenuse = AC/AB
Using the Pythagorean theorem, we can find the length of the hypotenuse AB:
AB^2 = AC^2 + CB^2
AB^2 = 7^2 + 24^2
AB^2 = 625
AB = 25
Therefore, we can calculate the cosine of ∠A as:
cos(∠A) = AC/AB = 7/25
Rounding to the nearest hundredth, we get:
cos(∠A) ≈ 0.28
Therefore, the value of the cosine of ∠A to the nearest hundredth is 0.28.