Questions: Use the triangle below to find cos(A).

Transcript text: Use the triangle below to find $\cos (A)$.

Solution

Solution Steps

Step 1: Find the hypotenuse

We are given a right triangle with legs of length 24 and 32. We need to find the length of the hypotenuse, _c_, using the Pythagorean theorem: $a^2 + b^2 = c^2$. In this case, $24^2 + 32^2 = c^2$, so $576 + 1024 = c^2$, which means $1600 = c^2$. Thus, $c = \sqrt{1600} = 40$.

Step 2: Calculate cos(A)

The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse. In this case, the side adjacent to angle A has length 24, and the hypotenuse has length 40. Therefore, cos(A) = adjacent/hypotenuse = 24/40.

Step 3: Simplify the fraction

The fraction 24/40 can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 8. So, 24/40 simplifies to 3/5.

Final Answer:

cos(A) = 3/5

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