2024年7月30日 · To get this result, use the formula area = a²√3/2, where a is the shorter leg of your triangle. Recall that the shorter leg is a half of the hypotenuse , so in our case a = 10 / 2 = 5 . Plugging this value into the area formula, we get area = 25√3/2 ≈ 21.65 .

A 30-60-90 triangle is a particular right triangle because it has length values consistent and in primary ratio. In any 30-60-90 triangle, the shortest leg is still across the 30-degree angle, the longer leg is the length of the short leg multiplied by the square root of 3, and the hypotenuse's size is always double the length of the shorter leg.

We've figured out the relationship between the short leg and hypotenuse of a 30-60-90 triangle, but what about the longer leg? How do we find that one? It's not quite as simple. There are two different ways to find the length of the long leg. One way is to use the Pythagorean Theorem. In this example, we have a right triangle that's missing a side.

In a right triangle, the hypotenuse is 12 cm, and the smaller angle is 30 degrees. Find the length of the long and short leg. Solution. Given the ratio of the sides = x: x√3:2x. 2x = 12 cm. x = 6cm. Substitute x = 6 cm for the long and short leg to get; Short leg = 6cm. long leg = 6√3 cm. Example 7. The two sides of a triangle are 5√3 mm ...

2023年1月11日 · Suppose you have a 30-60-90 triangle: We know that the hypotenuse of this triangle is twice the length of the short leg: We also know that the long leg is the short leg multiplied times the square root of 3: We set up our special 30-60-90 to showcase the simplicity of finding the length of the three sides. Try figuring this one out:

To calculate the side lengths of a 30-60-90 triangle, follow these steps: 1. Identify the known side length (leg or hypotenuse) and label it appropriately. Use the ratios of the sides in a 30-60-90 triangle to determine the lengths of the other sides. The …

A 30 -60-90 triangle is a special right triangle in which the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is the square root of 3 times the length of the shorter leg. Hypotenuse = 2 × shorter leg. Longer leg = √3 × shorter leg.

Using a short leg length of 1, long leg length of 2, and hypotenuse length of √3, the Pythagorean theorem is applied and gives us: 1 2 + (√3) 2 = 2 2, 4 = 4. The theorem holds true with the side lengths of a 30 60 90 triangle. Let's work through an example problem together to reinforce our understanding of 30 60 90 triangles.

Short Leg is half of the Hypotenuse. This example shows the easiest application of the patterns (where the hypotenuse is given). Always look at what is "given" and what you need to find. 1. Find x and y. This example requires more thinking and more algebraic work (where the short leg is …

As shown in the above image, the angles measure 30, 60, and 90 degrees. The formulas for the 30-60-90 special triangle are as follows: short leg=x; long leg=short leg*sqrt(3) hyp=short leg*2; This information tells us that in order to find the length of …