Answer:
b ≈ 10.1 in
x° = 32°
(2x -6)° = 58°
Step-by-step explanation:
The sum of angles of a triangle is 180°, so the acute angles in a right triangle are complementary.
x° +(2x -6)° = 90°
3x -6 = 90 . . . . . . simplify, divide by °
x -2 = 30 . . . . . divide by 3
x = 32
The acute angles are ...
x° = 32°
(2x -6)° = 58°
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The value of 'b' can be found using either the Pythagorean theorem or trig functions. We choose the Pythagorean theorem:
b² +3² = 10.5²
b² = 110.25 -9 = 101.25
b = √101.25 ≈ 10.1 . . . inches
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Additional comment
The attachments show the solution to this triangle will depend on your solution method. The numbers given are inconsistent, so no such triangle can be constructed.
