SOLUTION: One acute angle of a right triangle is not less than 30° more than twice the other acute angle. What are the possible measures of the larger angle?
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Question 1036322: One acute angle of a right triangle is not less than 30° more than twice the other acute angle. What are the possible measures of the larger angle? Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let the 2 acute angles of the right triangle be represented by a and b.
you get a + b = 90.
if a is not less than 2b + 30, then a must be greater than or equal to 2b + 30.
your equation is therefore a >= 2b + 30
since a + b = 90, then b = 90 - a and the equation becomes a >= 2 * (90 - a) + 30.
simplify this is to get a >= 180 - 2a + 30.
add 2a to both sides of the equation and combine like terms to get 3a >= 210.
divide both sides of this equation by 3 to get a >= 70.
if a >= 70, then b <= 20 because a + b = 90.
let's see how this works.
let's assume that a = 70.
this means that b = 20 and we get 2 * 20 + 30 = 70.
this satisfies the requirement that a is not less than 2 * b + 30 because a = 2 * b + 30, so we're good.
now let's look at a = 71 degrees.
this means that b = 19 degrees.
a >= 2 * b + 30 means 71 >= 2 * 19 + 30 which means that 71 >= 68.
this means that a is not less than 2 * b + 30 because a is greater than 2 * 19 + 30.
looks like the requirements of the problem are satisfied.
take any angle greater than or equal to 70 but less than or equal to 90 and the requirements of the problem will be satisfied.
lets take one look at a smaler than 70.
assume a = 69.
this makes b = 21.
2*b + 30 is equal to 42 + 30 = 72.
in this case a < 2 * b +30 because 69 is smaller than 72, so we're not good since a is not greater than or equal to 70.
the requirements are only satisfied when a is >= 70.
your solution is that the possible measures of the larger angle are 70 <= a <= 90, where a represents the larger angle.
You can put this solution on YOUR website!
One acute angle of a right triangle is not less than 30° more than twice the other acute angle. What are the possible measures of the larger angle?
