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What formulas are used with a right triangle? A right triangle is one in which one of the interior angles is a right angle. (90 degree angle) As a result, certain formulas allow you to calculate missing leg lengths and angles of right triangles.

Step 1 . Use tangent, which is Opposite/Adjacent.

so tan B = 3/7.

Step 2 . Use a calculator: tan^-1 (3/7) = 23 degrees for angle B

Step 3 . To find angle C, take the sum of a triangle which is 180, and subtract <B and <A

180 - 23 - 90 = 67 for angle C

Special Right Triangles

Right Triangle Properties VIDEO

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Right Triangle Formulas The Pythagorean Theorem is used to find the hypotenuse and leg lengths.

Step 1 . 3^2+7^2=c^2

Step 2 . 9+49= c^2

58= c^2

Step 3 . √58=c^2

7.2 =hypotenuse length

Trig Ratios

Sine = Opposite/Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite/Adjacent

Find the angle measures in triangle ABC.

Trig Ratios

Find missing lengths and angles in a right triangle

Area formula right triangle =1/2(leg x leg)

Perimeter formula a + b + c

Find the area of a right triangle

Find the perimeter of a right triangle

Find the hypotenuse of 30-60-90 Triangle

Find the longer leg of 30-60-90 Triangle

Find the shorter leg of 30-60-90 Triangle

Find the area of 30-60-90 Triangle

Find the hypotenuse of 45-45-90 triangle

Find the area of a 45-45-90 triangle

For example: Find the hypotenuse of triangle ABC.

What is the hypotenuse length of a 30-60-90 triangle with a short leg of 6 units? 2 x6 = 12 units

What is the longer leg length of a 30-60-90 triangle with a short leg of 6 units?

What is the shorter leg length of a 30-60-90 triangle with a hypotenuse of 6 units? 6/2 =3 units

Calculate the perimeter of triangle ABC

Calculate the area of a right triangle with leg lengths of 6 and 8 units.

1/2(6x8)

1/2*48 = 24 units

Find the hypotenuse of a 45-45-90 triangle with a leg length of 7.07. units

√2*7.07 =10 units

Find the leg length of a 45-45-90 triangle with a hypotenuse length of 10 units.

10/√2=7.07 units

Area = 1/2 (10.39 x 6)

1/2 x 62.34 = 31.17 units ^2

Area = 1/2 ( 6 x 6)

1/2 x = 36 =18 units^2

use the short side as the height and the long side as your base

Because of the ninty degree angle one leg can be the base and the other leg can be the height

30-60- 90 Triangles

45-45- 90 Triangles Find the leg of 45-45-90 triangle