Unit 8: Right Triangles Trigonometry Homework 2: Special Right Triangles...Please Help! 16. 16, 6 45 30 (2024)

FAQs

How do you find the answer to a special right triangle? ›

Solving right triangles

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. Pythagorean theorem: a² + b² = c². Sines: sin A = a/c, sin B = b/c. Cosines: cos A = b/c, cos B = a/c.

To find the hypotenuse, add the squares of the other sides, then take the square root. To find a shorter side, subtract the squares of the other sides, then take the square root.

The mnemonic SOHCAHTOA can be used to aid in remembering which function to use in what circ*mstance - SOH stands for Sine is opposite over hypotenuse; CAH stands for Cosine is adjacent over hypotenuse; and TOA stands for Tangent is opposite over adjacent. This will save confusion when working with these functions.

side-angle-side theorem, in Euclidean geometry, theorem stating that if two corresponding sides in two triangles are of the same length, and the angles between these sides (the included angles) in those two triangles are also equal in measure, then the two triangles are congruent (having the same shape and size).

The angle of depression is the angle one has to look down from the horizontal to see something on a lower level. The line of sight is the direct line from the observer to the object they are looking at, so for an angle of depression, the line of sight is angled down.

If you have an angle and the side opposite to it, you can divide the side length by sin(θ) to get the hypotenuse. Alternatively, divide the length by tan(θ) to get the length of the side adjacent to the angle.

The 45-45-90 triangle theorem is also called the Pythagorean theorem. In accordance with this theorem, legs a and b are the same value. To solve for the hypotenuse, use the equation c = a times the square root of 2. To solve for the legs, use the equation a = c divided by the square root of 2.

45 45 90 triangle sides

The legs of such a triangle are equal; the hypotenuse is calculated immediately from the equation c = a√2 . If the hypotenuse value is given, the side length will be equal to a = c√2/2 .

The formula for the 2 types of special right triangles is expressed in the form of the ratio of the sides and can be written as follows: 30° 60° 90° triangle formula: Short leg: Long leg : Hypotenuse = x: x√3: 2x. 45° 45° 90° triangle formula: Leg : Leg: Hypotenuse = x: x: x√2.