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angle measure right triangle
video tutorial right triangles
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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
right triangle 3 x7

Special Right Triangles

line
Pythagorean Theorem

Right Triangle Formula

leg
leg
hypotenuse

Right Triangle Formulas

The Pythagorean Theorem is used to find the hypotenuse and leg lengths.
right triangle 3 x7


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
angle measure right triangle
a
b
right triangle formula
a line
a line
3
7
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 
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



angle measure right triangle
​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

30-60- 90 Triangles

45-45- 90 Triangles

Find the leg of 45-45-90 triangle