How do you find the short side of a 30 60 90 triangle if you have the length of the long side?

How do you find the short side of a 30 60 90 triangle if you have the length of the long side?

Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg. Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side.

What is the shortest side of a 30 60 90 triangle if hypotenuse is 24?

In a 30-60-90 triangle, if the shortest side (the side opposite the 30° angle) has length x, then the side opposite the 60° angle has length √3 x and the length of the hypotenuse is 2x. So, if the hypotenuse has length 24√3, then the shorter leg has length (1/2)(24√3) = 12√3.

What is the length of the short leg in a 30 60 90 triangle with hypotenuse 1?

Again, we are given two angle measurements (90° and 60°), so the third measure will be 30°. Because this is a 30-60-90 triangle and the hypotenuse is 30, the shortest leg will equal 15 and the longer leg will equal 15√3.

What are the formulas for a 30 60 90 Triangle?

30-60-90 Triangle Ratio

• Short side (opposite the 30 degree angle) = x.
• Hypotenuse (opposite the 90 degree angle) = 2x.
• Long side (opposite the 60 degree angle) = x√3.

Which Triangle is a 30 60 90 Triangle?

special right triangle
The 30-60-90 triangle is called a special right triangle as the angles of this triangle are in a unique ratio of 1:2:3. Here, a right triangle means being any triangle that contains a 90° angle. A 30-60-90 triangle is a special right triangle that always has angles of measure 30°, 60°, and 90°.

What is the 30 60 90 triangle formula?

In a 30-60-90 triangle, the ratio of the sides is always in the ratio of 1:√3: 2. This is also known as the 30-60-90 triangle formula for sides. y:y√3:2y. Let us learn the derivation of this ratio in the 30-60-90 triangle proof section.

Which triangle is a 30 60 90 triangle?

What are the lengths of a 30 60 90 triangle?

In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg. To see why this is so, note that by the Converse of the Pythagorean Theorem, these values make the triangle a right triangle.

Which triangle is a 30 60 90 triangle quizlet?

What is right triangle is a triangle with angle measures of 30°, 60°, and 90°. In a 30°-60°-90° right triangle, the measure of the hypotenuse is twice the measure of the short leg, and the measure of the longer leg is the measure of the short leg times √3 . You just studied 2 terms!

Can 30 60 90 angles make a triangle?

What is a 30-60-90 Triangle? A 30-60-90 triangle is a right triangle with angle measures of 30º, 60º, and 90º (the right angle). Because the angles are always in that ratio, the sides are also always in the same ratio to each other.

Which is the shorter leg of a 30°-60°-90° triangle?

You can imagine a 30°-60°-90° triangle as an equilateral triangle that has been cut in half. One of the original base sides will be cut in half to form the short leg. So the short leg is exactly half the hypotenuse. Which means the hypotenuse is exactly twice as long as the short leg. 2 x 4 = 8.

How to calculate the hypotenuse of a triangle?

We know that the hypotenuse of this triangle is twice the length of the short leg: 3.46 k m 2 = 1.73 k m We also know that the long leg is the short leg multiplied times the s q u a r e r o o t o f 3: 1.73 × 3 ≈ 3 k m

What are the properties of the 30-60-90 triangle?

30-60-90 Triangle Theorem These three special properties can be considered the 30-60-90 triangle theorem and are unique to these special right triangles: The hypotenuse (the triangle’s longest side) is always twice the length of the short leg The length of the longer leg is the short leg’s length times 3

How to calculate the length of a right triangle?

In right-triangle trigonometry, a/h = sin Ө, where “a” is the length of the side opposite angle Ө, sin Ө is the value of the sine function for angle Ө, and h is the length of the hypotenuse. h = 8 is the length of the hypotenuse of a 30° – 60° – 90° triangle when the shorter leg has a length of 4.