  Master the 7 pillars of school success      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

leg
leg
hypotenuse

## 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

3
7 a
b     3
7
Trig Ratios

Sine = Opposite/Hypotenuse

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
2(shorter leg)
√3*(shorter leg)
hypotenuse/2
1/2 base x height
Find the hypotenuse of 45-45-90 triangle
√2* (leg)
hypotenuse/√2
1/2 base x height
Find the area of a 45-45-90 triangle
c
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?

√3*6 =  10.392 longer leg
What is the shorter leg length of a 30-60-90 triangle with a hypotenuse of   6 units?  6/2 =3 units ​6
​10
8
Calculate the perimeter of triangle ABC
6+8+10 = 24 units
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               6
10.39
12
Area = 1/2 (10.39 x 6)

1/2 x 62.34 = 31.17 units ^2 6
6
8.4
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

### 45-45- 90 Triangles

Find the leg of 45-45-90 triangle