So i am having a hard time with special right triangles and wanted to know how to solve problems such as: (45,45,90) and (30,30,60) problem. I know how to do it but need extra help.

are your 3 numbers in the bracket supposed to be angles?

if so then the first is an isosceles right-angled triangle, with sides in the ration of 1 : 1 : √2

the second one can't be triangle, since the sum of the 3 angles does not add up to 180
Was it supposed to be 30, 60, 90 ?
If so, then it is a right-angled triangle with sides in the ratio 1 : √3 : 2

Darren works 8 hours a day, five days a week, for 52 weeks a year, how many hours will he have worked after 15 years?

Special right triangles, such as the 45-45-90 and 30-60-90 triangles, have specific ratios between their sides that can help make solving problems involving them easier. Let's go through each triangle separately.

1. 45-45-90 Triangle:
In a 45-45-90 triangle, the two legs (the sides opposite the 45 degree angles) are congruent, and the hypotenuse (the side opposite the 90 degree angle) is the longest side. The ratio between the sides of this triangle is 1 : 1 : √2.

To solve problems involving this triangle, you can follow these steps:
Step 1: Identify the known side lengths.
Step 2: Use the ratios to find the missing side lengths.

For example, if you know one leg is 3 units long, you can solve for the other leg and the hypotenuse:
- Leg length = 3 units
- Find the other leg: Since the two legs are congruent, the other leg is also 3 units long.
- Find the hypotenuse: Use the ratio 1 : √2. Multiply the leg length by √2: 3 * √2 ≈ 4.24 (rounded to two decimal places).

2. 30-60-90 Triangle:
In a 30-60-90 triangle, the side opposite the 30 degree angle is half the length of the hypotenuse, and the side opposite the 60 degree angle is (√3)/2 times the length of the hypotenuse. The ratio for this triangle is 1 : (√3)/2 : 1/2.

To solve problems involving this triangle, you can follow these steps:
Step 1: Identify the known side lengths.
Step 2: Use the ratios to find the missing side lengths.

For example, if you know the shorter leg is 4 units long, you can solve for the other leg and the hypotenuse:
- Short leg length = 4 units
- Find the other leg: Use the ratio (√3)/2. Multiply the short leg length by (√3)/2: 4 * (√3)/2 ≈ 3.46 (rounded to two decimal places).
- Find the hypotenuse: Use the ratio 1. Multiply the short leg length by 2: 4 * 2 = 8.

Understanding and memorizing these ratios will help you quickly solve problems involving special right triangles. Remember to use the ratios that correspond to the specific triangle you are working with.