1.) If c=12√3 cm, then a=___ and b=___.

2.) A refrigerator has a width of 3 feet. The angle of elevation from the bottom corner to the opposite corner is 65º. What is the height of the refrigerator?

3.) In a 30-60-90 triangle, the shorter leg has length of 8√3 m. Find the length of the other leg (L) and the hypotenuse (H).

1) More information or a figure is needed. I also can't interpet your

√3 symbol

2) 3.0/cos65 feet

3) In a 30-60-90 triangle, the shortest leg is half the hypotentuse

If c=12√3 cm, then a=___ and b=___.

well this is for problem has a 30, 60,90 triangle.
But thanks:)

Then you use (alt + number keypad entries) to type exotic math symbols, they often do not appear on all computers. That is what is happeing with your √3 symbol

1.) To find the values of a and b in the equation c = 12√3 cm, we need to understand the relationship between the sides of a right triangle.

In a right triangle, the Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

c^2 = a^2 + b^2

In this case, we are given the value of c as 12√3 cm. To find the values of a and b, we can substitute c into the equation:

(12√3)^2 = a^2 + b^2

Simplifying, we have:

144 * 3 = a^2 + b^2

432 = a^2 + b^2

Now, let's solve for a and b. However, we need more information to find the specific values of a and b.

2.) To find the height of the refrigerator, we will use trigonometry. We are given the width of the refrigerator as 3 feet and the angle of elevation from the bottom corner to the opposite corner as 65º. Let's assume that the height of the refrigerator is h.

In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height (h) and the adjacent side is the width (3 feet).

So, we have:

tan(65º) = h / 3

To find the value of h, we can rearrange the equation:

h = 3 * tan(65º)

Using a calculator, we can evaluate the right side of the equation to find the height of the refrigerator.

3.) In a 30-60-90 triangle, the sides are related by specific ratios.

The ratio of the length of the shorter leg to the hypotenuse is 1 : 2√3 : 2.

We are given the length of the shorter leg as 8√3 m.

To find the length of the other leg (L), we can use the ratio:

L = (1/2) * (8√3) = 4√3 m

To find the length of the hypotenuse (H), we can use the ratio:

H = 2 * (8√3) = 16√3 m

So, the length of the other leg (L) is 4√3 m and the length of the hypotenuse (H) is 16√3 m.