Special Right Triangles Worksheet

Are you a teacher or a student in need of practice with special right triangles? Look no further than this special right triangles worksheet! Designed specifically for those learning about or reviewing this topic, this worksheet focuses on the concept of special right triangles and their properties.

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Name two special right triangles.

Two special right triangles are the 45-45-90 triangle, which has angles of 45 degrees, 45 degrees, and 90 degrees, and the 30-60-90 triangle, which has angles of 30 degrees, 60 degrees, and 90 degrees.

What is the ratio of the lengths of the sides in a 45-45-90 triangle?

In a 45-45-90 triangle, the ratio of the lengths of the legs to the length of the hypotenuse is 1:1:?2. This means that the lengths of the two legs are equal, and each is equal to ?2 times the length of the hypotenuse.

What is the ratio of the lengths of the sides in a 30-60-90 triangle?

In a 30-60-90 triangle, the ratio of the sides is 1:?3:2, where the side opposite the 30-degree angle is 1, the side opposite the 60-degree angle is ?3, and the hypotenuse is 2 times the length of the side opposite the 30-degree angle.

How can you find the length of the hypotenuse in a 45-45-90 triangle if the length of one leg is given?

In a 45-45-90 triangle, the two legs are congruent, and the length of the hypotenuse can be found by multiplying the length of one leg by the square root of 2. So, if the length of one leg is given, you can find the length of the hypotenuse by multiplying the length of the leg by ?2.

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

To find the length of the longer leg in a 30-60-90 triangle when the length of the shorter leg is given, you can use trigonometric functions. In a 30-60-90 triangle, the ratio of the shorter leg to the longer leg is 1:?3. So, if you know the length of the shorter leg, you can multiply it by ?3 to find the length of the longer leg. For example, if the shorter leg is 6 units long, then the longer leg would be 6?3 units long.

What is the relationship between the angles in a 45-45-90 triangle?

In a 45-45-90 triangle, which is an isosceles right triangle, the two acute angles are both 45 degrees, and the right angle is 90 degrees. Therefore, the relationship between the angles in a 45-45-90 triangle is that the two acute angles are congruent and each measure 45 degrees, while the right angle measures 90 degrees.

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

In a 30-60-90 triangle, the angles are always 30 degrees, 60 degrees, and 90 degrees. The relationship between these angles is that the side opposite the 30-degree angle is half the length of the side opposite the 60-degree angle, and the side opposite the 90-degree angle (the hypotenuse) is the longest side and is always the square root of three times the length of the side opposite the 30-degree angle. This relationship can be expressed using trigonometric functions and is a characteristic property of any 30-60-90 triangle.

How can you check if a triangle with given side lengths is a special right triangle?

To check if a triangle with given side lengths is a special right triangle, you can use the Pythagorean theorem. For a right triangle to be a special right triangle, the squares of the shorter two sides should add up to be equal to the square of the longest side. In the case of a 3-4-5 triangle, for example, you would check if \(3^2 + 4^2 = 5^2\) holds true. If the equation is satisfied, then the triangle is a special right triangle, otherwise, it is a regular right triangle.

What are the measures of the angles in a 45-45-90 triangle?

In a 45-45-90 triangle, the measures of the angles are 45 degrees for each of the two acute angles and the remaining angle, which is the right angle, is 90 degrees.

What are the measures of the angles in a 30-60-90 triangle?

The measures of the angles in a 30-60-90 triangle are 30 degrees, 60 degrees, and 90 degrees. The triangle is named based on the degree measures of its angles, with the sides in ratio of 1:?3:2 across from the 30°, 60°, and 90° angles, respectively.