David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. These special right triangles also have formulas to simplify solving them.Ī 30 60 90 triangle is a special right triangle with 30° and 60° interior angles adjacent to the right 90° angle.This article was co-authored by David Jia. There are a few types of special right triangles, which are triangles that have specific proportions. You can use the formulas above to find the lengths of the missing leg or hypotenuse if any are missing. The perimeter is equal to leg a plus leg b plus hypotenuse c. The formula to find the perimeter of a right triangle is: Keep in mind that in the above formulas, angle β must be adjacent to leg a, and angle α must be adjacent to leg b. The area A of a right triangle is equal to leg a squared times one-half the tangent of angle β, or leg b squared times one-half the tangent of angle α. Given the value of leg b and angle α, find the area using the following formula: Given the value of leg a and angle β, find the area using the following formula: If you know the length of one leg and the value of an adjacent angle, then you can use the tangent function to find the area. Method Three: Using One Leg and One Angle Notice the √(c² – a²) portion of this formula is simply the Pythagorean theorem isolated for b. The area A of a right triangle is equal to leg a times 1/2 times the square root of the hypotenuse c squared times minus leg a squared. If you know the hypotenuse and one of the legs, then you can use a variation of the Pythagorean theorem to find the area: The area A of a right triangle is equal to one-half times leg a times leg b. If you know the length of the two legs in a right triangle, then you can find the area using the formula: There are a few methods to find the area of a right triangle. Learn more about using this mnemonic on our SOHCAHTOA calculator. SOH: sin(θ) = opposite ÷ hypotenuse CAH: cos(θ) = adjacent ÷ hypotenuse TOA: tan(θ) = opposite ÷ adjacent If you split SOHCAHTOA into three parts, each part represents one of the formulas, where each letter is the first letter in the part of the equation. You can use the mnemonic SOHCAHTOA to help remember the equations above. Subtract 90° (because this is a right triangle, we know one of the angles is 90°) and the angle you just found from 180 to find the missing angle. You can also use the special rule of triangles where the sum of all angles must equal 180°. The first way is to repeat using the same method as before, but with a different formula to find the remaining angle. You can find the remaining angle in a few ways. Note, in the above example, the inverse of cosine was used in the second to last question to isolate θ. So, for a right triangle with angle θ, with an adjacent side length of 7 and hypotenuse of 15, the angle θ is 62.18°. Start by choosing the equation using adjacent and hypotenuse: cos(θ) = adjacent ÷ hypotenuseĬos(θ) = 7 ÷ 15 cos(θ) = 0.4667 θ = cos -1(0.4667) θ = 62.18° For example, let’s find the angle of a triangle if the adjacent side length is 7 and the hypotenuse is 15.
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