Angles α and β are the two acute angles in a right triangle, where α = 5x 3 + 20 and β = 2x 3 + 14. Find α.
2 answers:
The acute angles of a right triangle are complementary, so
α + β = 90
(5x/3 +20) + (2x/3) + 14) = 90 . . . . . . substitute given values
7x/3 +34 = 90 . . . . . . . . . . . . . . . . . . . collect terms
7x/3 = 56 . . . . . . . . . . . . . . . . . . . . . . . subtract 34
x = (3/7)*56 = 24 . . . . . . . . . . . . . . . . . multiply by 3/7
Then the value of α is ...
α = 5*24/3 +20 = 60
Answer:
α = 56° is the answer.
Step-by-step explanation:
In a triangle sum of all angles = 180°
Since it's a right angle triangle therefore
α + β + 90° = 180°
α + β = 180 - 90 = 90°
Now we put the values of α and β given in the question.
α = 5x³ + 20 , β = 2x³ + 14
Equation becomes
5x³ + 20 + 2x³ + 14 = 90
7x³ + 34 = 90
7x³ = 90 - 34 = 56
x³ = 56/7 = 8
x³ = 2³
therefore x = 2
Now we put the value of x in angle α
α = 5x³ + 14 = 5×2³ + 14
α = 5×8 + 14 = 40 + 14 = 56
α = 56°
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