If one angle of a triangle is 2/3 x grades and another is 3/2x degrees while the third is π/75x radians, then the measures of angles are
a) 24°, 60°, 96°
b) 96°, 60°, 24°
c) 20°, 50°, 110°
d) 20°, 60°, 100°
Answers
Answer:
Yes
Step-by-step explanation:
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Answer:
Given as One angle of a triangle is 2x/3 grades and another is 3x/2 degree while the third is πx/75 radians. As we know that, 1 grad = (9/10)° 2/3x grad = (9/10) (2/3x)° = 3/5x° As we know that, π rad = 180° ⇒ 1 rad = 180°/π Also given as πx/75 (πx/75 × 180/π)° (12/5x)° As we know that, the sum of the angles of a triangle is 180°. 3/5x° + 3/2x° + 12/5x° = 180° (6 + 15 + 24)/10x° = 180° Now, upon cross-multiplication we get, 45x° = 180° × 10° = 1800° x° = 1800°/45° = 40° Thus, the angles of the triangle are 3/5x° = 3/5 × 40° = 24° 3/2x° = 3/2 × 40° = 60° 12/5 x° = 12/5 × 40° = 96°Read more on Sarthaks.com - https://www.sarthaks.com/651861/angle-triangle-grades-another-degrees-while-third-radians-express-all-the-angles-degrees
Step-by-step explanation:
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