Example: Trig to solve the sides and angles of a right triangle | Trigonometry | Khan Academy

Recent questions

• What is a right triangle?

  A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. This specific angle is known as the right angle, and it distinguishes right triangles from other types of triangles, such as acute and obtuse triangles, which have angles less than or greater than 90 degrees, respectively. In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are referred to as the legs. Right triangles are fundamental in geometry and trigonometry, as they allow for the application of various mathematical principles, including the Pythagorean theorem and trigonometric ratios, which relate the angles and sides of the triangle.

• How do you calculate the hypotenuse?

  To calculate the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is expressed as c² = a² + b². To find the hypotenuse, you would first measure the lengths of the two legs of the triangle, square each of those lengths, add the results together, and then take the square root of that sum. This method provides a straightforward way to determine the length of the hypotenuse, which is the longest side of the triangle, ensuring accurate calculations in various applications, from construction to navigation.

• What is the tangent function?

  The tangent function is a fundamental trigonometric function that relates the angles of a right triangle to the ratios of its sides. Specifically, for a given angle in a right triangle, the tangent of that angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Mathematically, it is expressed as tan(θ) = opposite/adjacent. The tangent function is particularly useful in various fields, including physics, engineering, and architecture, as it allows for the calculation of unknown side lengths or angles when certain measurements are known. Additionally, the tangent function is periodic and can be graphed, showing its behavior across different angles, which is essential for understanding wave patterns and oscillations.

• How do you find an angle in a triangle?

  To find an angle in a triangle, especially in a right triangle, you can use the triangle angle sum property, which states that the sum of the interior angles of any triangle is always 180 degrees. In a right triangle, one angle is already 90 degrees, so you can find the other angles by subtracting the known angles from 180 degrees. For example, if you know one angle measures 65 degrees, you can find the other angle by calculating 180° - 90° - 65° = 25°. Alternatively, if you have the lengths of the sides, you can use trigonometric functions such as sine, cosine, or tangent to determine the angles based on the ratios of the sides. This approach is particularly useful in solving problems where direct measurement of angles is not possible.

• What is the Pythagorean theorem?

  The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship is expressed mathematically as c² = a² + b², where c represents the hypotenuse, and a and b represent the other two sides. The theorem is widely used in various applications, including construction, navigation, and physics, as it provides a method for calculating distances and verifying the right angle in triangles. Its simplicity and effectiveness make it a cornerstone of trigonometry and geometry, allowing for the resolution of many practical problems involving right triangles.