in ABC A=30

a=9
b=8
this triangle must be
1)right triangle
2 acute
3 obtuse
4 either acute or obtuse

Why do you show lengths of two a's?

One is <A 30 degrees and a is 9 cm

I got obtuse for the answer

Agree, I got angle C >90°

btw, choice 4 is rather silly,
because it is also a correct choice.

After doing your 3:00 pm post, I realized that you are working with the ambiguous case

so angle B could be either 26.4° or 153.6°

so the triangle could be either acute OR obtuse, choice #4

To determine whether the triangle is a right triangle, acute, obtuse, or either acute or obtuse, we need to use the Pythagorean theorem.

First, let's calculate the value of the third side of the triangle (side C) using the Pythagorean theorem:
c^2 = a^2 + b^2

Given that a = 9 and b = 8, we can substitute those values into the equation:
c^2 = 9^2 + 8^2
c^2 = 81 + 64
c^2 = 145

To find the value of c, we need to take the square root of both sides:
c = √145
c ≈ 12.04

Now, let's analyze the lengths of the sides. We have a = 9, b = 8, and c ≈ 12.04.

To determine the type of triangle, we need to compare the squares of the lengths of the sides:

1) If a^2 + b^2 = c^2, then the triangle is a right triangle.
In our case, 9^2 + 8^2 = 81 + 64 = 145, which is not equal to c^2. Therefore, the triangle is NOT a right triangle.

2) If a^2 + b^2 > c^2, then the triangle is acute.
In our case, 9^2 + 8^2 = 81 + 64 = 145, which is equal to c^2 (approximately 12.04^2). Therefore, the triangle is ACUTE.

3) If a^2 + b^2 < c^2, then the triangle is obtuse.
In our case, 9^2 + 8^2 = 81 + 64 = 145, which is equal to c^2 (approximately 12.04^2). Therefore, the triangle is NOT obtuse.

Therefore, this triangle is acute (option 2).