In a right triangle, the sum of the angles is 180°, and one of the angles is already 90°. To find the missing angle, we will use the cosine rule and the inverse cosine function.
Let’s identify the sides:
- The longest side (hypotenuse) is 65.
- The other two sides are 56 and 33.
We'll assume we're looking for the angle opposite to the side of length 33. We will use the formula:
\[ \cos(A) = \frac{\text{adjacent side}}{\text{hypotenuse}} \]
In this case, the adjacent side to angle A is 56, and the hypotenuse is 65.
Now, let's calculate:
\[ \cos(A) = \frac{56}{65} \]
Next, we calculate the value of \(\cos(A)\):
\[ \cos(A) \approx 0.8615 \]
Now, we find the angle A using the inverse cosine:
\[ A = \cos^{-1}(0.8615) \]
Calculating that:
\[ A \approx 30.5° \]
Thus, the approximate measure of the missing angle is:
30.5°
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