Special Right Triangles
Isosceles Right Triangle
30-60-90 Triangle
help 1-12 please

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

1.

since it is a right-angled triangle, and one of the leg angles is 45°, then the other leg angle is also 45°.

which makes this an isoceles triangle.

so, the second leg is 6 too.

the baseline (Hypotenuse) is then per Pythagoras

baseline² = 6² + 6² = 36 + 36 = 72 or 2×36

baseline = sqrt(72) = 6×sqrt(2)

2.

this is then a 30-60-90 triangle.

the left leg (a) is then 2a/2 = 10/2 = 5.

and the bottom leg is 5×sqrt(3).

3.

isoceles triangle.

so, left and right legs (a) are both 3 (from the 3×sqrt(2)).

4.

30-60-90 triangle

upper leg is then 6×sqrt(3).

the baseline is 2 times the left leg : 2×6 = 12

5.

isoceles triangle

both legs are 2 (from the 2×sqrt(2)).

6.

30-60-90 triangle

left leg is 4 (from the 4×sqrt(3)).

the baseline is 2×4 = 8.

7.

isoceles triangle.

6 = a×sqrt(2)

a (both legs) = 6/sqrt(2)

8.

30-60-90 triangle

9 = a×sqrt(3)

a (left leg) = 9/sqrt(3)

baseline = 2a = 2×9/sqrt(3) = 18/sqrt(3)

9.

due to the equal leg angles this is an isoceles triangle.

4 = a×sqrt(2)

a (both legs) = 4/sqrt(2)

10.

30-60-90 triangle

the bottom leg (a) = 2a/2 = 6/2 = 3

the left leg is then 3×sqrt(3)

11.

isoceles triangle

left leg is also 5.

baseline is 5×sqrt(2)

12.

30-60-90 triangle

12 = a×sqrt(3)

a (left leg) = 12/sqrt(3)

the baseline is then 2a = 2×12/sqrt(3) = 24/sqrt(3)

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: