How do you solve a 30 60 90 triangle when given the hypotenuse?

How do you solve a 30 60 90 triangle when given the hypotenuse?

In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, and you can find the length of the long leg by multiplying the short leg by the square root of 3.

What is the hypotenuse length of a 30 60 90 Triangle?

40 feet
Now we know that the hypotenuse (longest side) of this 30-60-90 is 40 feet, which means that the shortest side will be half that length. (Remember that the longest side is always twice— 2 x —as long as the shortest side.)

What is the length of the shorter leg of a 30 60 90 right triangle if the length of the hypotenuse is 18?

In a 30-60-90 triangle, the shortest side (the side opposite the 30° angle) is always half as long as the hypotenuse. So the shortest side has length 9.

What is the length of the hypotenuse of a 30 60 90 right triangle if the short leg is five?

10 in
Given : short leg = 5 in. ∴ other leg =√3⋅5=5√3 in. Hypotenuse =2⋅5=10 in.

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.

What is the 30-60-90 Triangle Theorem?

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.

What is the perimeter of 30-60-90 Triangle?

perimeter equals 30.05 in – adding all sides gives that result perimeter = a + a√3 + 2a = a(3 + √3) ≈ 30.05 in.

How do you solve for the hypotenuse and longer leg of a 30-60-90 Triangle If the measurement of the shorter leg is given?

30-60-90 Triangle Theorem

1. The hypotenuse (the triangle’s longest side) is always twice the length of the short leg.
2. The length of the longer leg is the short leg’s length times √3.
3. If you know the length of any one side of a 30-60-90 triangle, you can find the missing side lengths.

What is the formula for 30-60-90 Triangle?

What is the length of the hypotenuse of a 30-60-90 right triangle if the length of the shorter leg is 6 cm?

The longest side, the hypotenuse, is 12 cm (so, n=6 cm) and the longer leg is 6√3 cm. In this type of triangle, the shorter of the two legs is one half of the hypotenuse (6, in this case), and that short leg is multiplied by the square root of 3 to obtain the length of the longer leg: 6√3.

Which angle in a 30-60-90 Triangle is the opposite of hypotenuse?

30- degree angle
From the illustration above, we can make the following observations about the 30-60-90 triangle: The shorter leg, which is opposite to the 30- degree angle, is labeled as x. The hypotenuse, which is opposite to the 90-degree angle, is twice the shorter leg length (2x).

Which Triangle is a 30-60-90 Triangle quizlet?

Special Right Triangles (30-60-90/45-45-90)

How to calculate the length of a 30-60-90 triangle?

The ratio of the side lengths of a 30-60-90 triangle are: 1 The leg opposite the 30° angle (the shortest side) is the length of the hypotenuse (the side opposite the 90° angle). 2 The leg opposite the 60° angle is of the length of the hypotenuse. 3 The hypotenuse is twice the length of the shortest side.

How to calculate the hypotenuse of a right triangle?

Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²) Given angle and one leg. c = a / sin(α) = b / sin(β), from the law of sines. Given area and one leg.

Which is the smallest side of the 30° 60° 90° triangle?

Note that the smallest side, 1, is opposite the smallest angle, 30°; while the largest side, 2, is opposite the largest angle, 90°. (Theorem 6). (For, 2 is larger than . Also, while 1 : : 2 correctly corresponds to the sides opposite 30°-60°-90°, many find the sequence 1 : 2 : easier to remember.)

Is the Pythagorean theorem applicable to the 30-60-90 triangle?

The concept of similarity can therefore be used to solve problems involving the 30-60-90 triangles. Since the 30-60-90 triangle is a right triangle, then the Pythagorean theorem a 2 + b 2 = c 2 is also applicable to the triangle.