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What are the three sides of a right triangle called?
Legs and hypotenuse.
State the Pythagorean theorem and explain its significance in right triangles.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs (). It’s significant for determining the relationships between the sides of a right triangle.
How do you determine if a triangle is a right triangle without measuring angles?
If the square of the length of the longest side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
What is the relationship between the legs and the hypotenuse in a right triangle?
The square of the hypotenuse is equal to the sum of the squares of the legs.
Explain the concept of the converse of the Pythagorean theorem.
The converse of the Pythagorean theorem states that if the square of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.
Can a right triangle have two sides of equal length? Explain.
Yes, a right triangle can have two sides of equal length. These triangles are called isosceles right triangles.
How do you find the length of a missing side in a right triangle if you know the lengths of the other two sides?
You can use the Pythagorean theorem () to find the missing side.
What is the trigonometric ratio commonly used to find angles in a right triangle?
Trigonometric ratios such as sine, cosine, and tangent are commonly used to find angles in a right triangle.
How can you use the sine, cosine, and tangent functions to find missing side lengths or angles in a right triangle?
Trigonometric functions help in establishing relationships between angles and sides in a right triangle to find missing measures.
What is the concept of a “45-45-90 triangle” and how does it apply to right triangles?
A “45-45-90 triangle” is an isosceles right triangle where its two acute angles are 45 degrees each, making the third angle a right angle of 90 degrees. In this triangle, the sides opposite the 45-degree angles are equal in length, and the hypotenuse is √2 times longer than the legs
Provide examples of real-life applications where knowledge of right triangles and the Pythagorean theorem is useful.
Real-life applications of right triangles and the Pythagorean theorem include determining distances, such as in navigation and surveying, calculating heights or distances in construction, and in various fields like physics, engineering, architecture, and astronomy for measurements and calculations involving right-angled scenarios.
Describe the special properties of the angles in a right triangle.
In a right triangle, one angle is always 90 degrees, while the other two angles are acute and complementary