30-60-90 Triangles

Front

What are the side lengths of a 30-60-90 triangle in relation to each other?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 : √3 : 2. The side opposite the 30° angle is the shortest (1), the side opposite the 60° angle is √3 times the shortest, and the hypotenuse is twice the shortest side.

Front

How do you find the length of the longer leg in a 30-60-90 triangle if the shorter leg is known?

Back

To find the length of the longer leg (opposite the 60° angle), multiply the length of the shorter leg (opposite the 30° angle) by √3.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what are the lengths of the other two sides?

Back

The shorter leg (opposite the 30° angle) is 5, and the longer leg (opposite the 60° angle) is 5√3.

Front

What is the formula to calculate the area of a 30-60-90 triangle?

Back

The area of a 30-60-90 triangle can be calculated using the formula: Area = (1/2) * base * height. Here, the base can be the shorter leg and the height can be the longer leg.

Front

What is the relationship between the angles and the sides in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the angles are always 30°, 60°, and 90°, and the sides are in a fixed ratio of 1 : √3 : 2.

Front

How do you derive the lengths of the sides in a 30-60-90 triangle from the shortest side?

Back

If the shortest side (opposite the 30° angle) is 'x', then the longer leg (opposite the 60° angle) is 'x√3' and the hypotenuse is '2x'.

Front

What is the value of the longer leg if the shorter leg of a 30-60-90 triangle is 4?

Back

If the shorter leg is 4, the longer leg is 4√3.

Front

In a 30-60-90 triangle, if the hypotenuse is 12, what is the length of the shorter leg?

Back

If the hypotenuse is 12, the shorter leg (opposite the 30° angle) is 6.

Front

What is the significance of the 30-60-90 triangle in real-world applications?

Back

30-60-90 triangles are often used in construction, architecture, and various fields of engineering due to their predictable side ratios.

Front

How can you use the properties of a 30-60-90 triangle to solve for unknown sides?

Back

You can use the known ratios of the sides (1 : √3 : 2) to set up equations based on the lengths of the sides you know to find the unknown lengths.