math help?

Question

In a right triangle ABC angleC=3y-10, angleB=y+40, and angleA=90. What type of right triangle is triangle ABC?

(1) scalene
(2) isosceles
(3) equilateral
(4) obtuse

Answer 1

The three angles must equal 180, so add them all together:
A = 90
B = y + 40
C = 3y - 10

Sum A + B + C = 180:
4y + 120 = 180
4y = 60
y = 15

Now plug this back into your other equations to figure the actual angles:
A = 90
B = 55
C = 35

None of the angles are the same so this eliminates isosceles or equilateral. And none of your angles are greater than 90 (angles in a right triangle are never obtuse) so that eliminates obtuse. There's only one answer left.

All the angles are different, so the answer is (1) scalene.

Answer 2

Since a triangle has angles that add up to 180 degrees and angleA is 90 degrees, we know that angleB+angleC= 90 degrees. y+40 +3y-10=90
4y+30=90
4y=60
y=15
Plug in 15 to equations for angleB and angleC to get the values
angleB=y+40
angleB=15+40
angleB=55

angleC=3y-10
angleC=3(15)-10
angleC=45-10
angleC=35

The triangle must be scalene. It is impossible for a right triangle to be obtuse or equilateral. For it to be isosceles angle B and C must be the same. They arent so it is scalene.

Answer 3

Since the total of all 3 angles of a triangle is 180 degree, and A is 90 degree, then B + C is 90, and thus 90 = 3y -10 + y + 40, which is 90 = 4 y + 30, or y=15. Thus angle C is 35 and B is 55 degree.
Since no angle is greater than 90 degree, it is not an obtuse triangle, since all 3 angles are not 60 degree, it is not equilateral, and since there are no 2 angles that are the same, it is not isoceles.
The only choice left is (1) scalene.

Answer 4

the answer is scalene. The triangle is scalene because when you set up the equation you get

(3y-10)+(y+40)+90=180.

the equation is equal to 180 because a triangle's angles total 180 degrees. You solve for y and get 15 so the other two angles equal 35 and 55. Thus none of the angles are equal and the triangle is scalene

Answer 5

To be a triangle ( on a plane ) all the internal angles need to add up to 180 degrees. so angleC+angleB must add to 90 degrees and you can eliminate equilateral.
So 4y+30 = 90 therefore y=15 degrees.
not isosceles either.

Over to you.

Answer 6

The triangle is scalene because when you simplify the 3y-10 and stuff, you'll find three different angles. Thus, it is a scalene triangle because scalene has no equal sides. It could be a obtuse triangle, but since none of the angles were more than 90, it would be scalene.

Answer 7

(1) scalene