Answer :
Final answer:
To find the unknown angle A in right triangle DEF, we use the fact that the sum of angles in a triangle is 180 degrees. Using the cosine rule, we first calculate the value for angle D and come up with an approximate of 57.12 degrees. Subtraction from a total of 180 degrees gives a result of approximately 32.88 degrees for angle A.
Explanation:
To answer the question, we must first understand that in a right triangle, the sum of the angles is always 180 degrees. Noting that angle F is a right angle (90 degrees), and you're given two other angles: angle D (a degrees) and angle E (b degrees). The value of angle A can be found by subtracting the known angles from the total degrees in a triangle. In other words, a + b + A = 180.
However, in this problem, the lengths of segments FD and FE are given instead of angles a and b. Trigonometry can be used to find these angles. The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. Therefore, you can find angle D as cos^-1(FD/FE).
Substituting the given values, angle D becomes cos^-1(30/55). This gives an approximate value for D that is 57.12 degrees.
Since we have angle D and angle F (which is 90 degrees), we can now calculate angle A (angle E), which should be A = 180 – 90 - 57.12. Therefore, angle A is 32.88 degrees. However, this isn't among the options given. Therefore, there might be a typo or an error in the question or the given choice of answers.
Learn more about Angles in a Right Triangle here:
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