Trigonometry, question about two angles in a right triangle, can you help?

Question

Let alpha and beta be two angles in a right triangle (niether alpha and beta is the right angle. Is it possible to have alpha + Beta(7)= 30degrees? Can you explain it to me, beta is multiplied by seven if it not clear.

Answer 1

The three angles must add up to 180 in a triangle
alpha + beta + 90 = 180

So alpha + beta will always be 90 degrees.

You now have two equations:
a + b = 90
a + 7b = 30

Subtract the top equation from bottom:
6b = -60

Divide by 6 on both sides:
b = -10
a = 100

So this is only possible if alpha is 100 degrees and beta is -10 degrees which is completely impossible!

Another way to see this. You have alpha + beta being 90 degrees.

alpha + beta = 90

Now add 6 more betas to both sides... and the number should get smaller on the right? How can adding 6 of something get you a smaller number. Again it isn't possible.

Answer 2

Well the total number of degrees in a triangle has to be 180. Since alpha and beta are the two angles that are not right angles, their sum has to equal 180 - 90 = 90.

So, I'll just use a and b for alpha and beta.

Your question is if this is possible:

a + 7b = 30 (equation 1)
when
a + b = 90 (equation 2)

Solve both equations for a:
Eqn 1 becomes
a = 30 - 7b (equation 3)
Eqn 2 becomes
a = 90 - b (equation 4)

Set equations 3 and 4 equal since they are both equal to a:
30 - 7b = a = 90 - b

Cut out the middle man and solve for b:
-60 = 6b
b = -10

Since an angle inside a triangle cannot be negative, a + 7b cannot equal 30.

Answer 3

No, it is not possible. If alpha + 7beta = 30 degrees, and adding the third angle, which is the right angle, it will only give 120 degrees. For a triangle to be formed, it must be exactly 180 degrees. Unless it is a special type of triangle (i.e., triangles is space).

Answer 4

You know that the three angles have to add up to 180°, and one of them is a right angle. That leaves α+β=90°. Subtract this from
α+7β=30° to eliminate the α term:
6β = -60°
β = -10° which isn't possible in a triangle.

Answer 5

well in with angles, 360 may as well be 0
so
a +7b = 360n +30
where n is an integer
so it is possible

so b is 50 a is 40