Instruction

1

You can find out the size of the third

b2 = a2 - c2;

c2 = a2 - b2

For example, a rectangular

S2 = 182 - 142 = 324 - 196 = 128 cm

c = √128 cm

Answer: the length of the second leg is √128 cm or approximately 11.3 cm

**parties**, knowing the lengths of two other sides**of the triangle**. This can be done by using the Pythagorean theorem, which States that the square of the hypotenuse of a rectangular**triangle**is equal to the sum of the squares of the other two sides. (a2 = b2+ c2). Hence, we can Express the lengths of all sides of a rectangular**triangle**:b2 = a2 - c2;

c2 = a2 - b2

For example, a rectangular

**triangle**are known, the length of the hypotenuse a (18 cm) and one of the legs, for example c (14 cm). To find*the length of the*other leg, you want to make 2 algebraic operations:S2 = 182 - 142 = 324 - 196 = 128 cm

c = √128 cm

Answer: the length of the second leg is √128 cm or approximately 11.3 cm

2

You can resort to another method if you know the length of the hypotenuse and the magnitude of one of the acute angles of the rectangular

a = s*sinα;

b = s*cosα.

Example: the length of the hypotenuse is 15 cm, one of the acute angles is 30 degrees. To find the lengths of the other two sides you need to perform 2 steps:

a = 15*sin30 = 15*0.5 = 7.5 cm

b = 15*cos30 = (15*√3)/2 = 13 cm (approx)

**triangle**. Let the length of the hypotenuse equal to c, one of the acute angles equal to α. In this case, find the 2 other**side of**rectangular**triangle**will be using the following formulas:a = s*sinα;

b = s*cosα.

Example: the length of the hypotenuse is 15 cm, one of the acute angles is 30 degrees. To find the lengths of the other two sides you need to perform 2 steps:

a = 15*sin30 = 15*0.5 = 7.5 cm

b = 15*cos30 = (15*√3)/2 = 13 cm (approx)

3

The most trivial way to find

P = a + b + c, where P is the perimeter of a rectangular

*the length of***sides**of a rectangular**triangle**is to Express it from the perimeter of this shape:P = a + b + c, where P is the perimeter of a rectangular

**triangle**. From this expression it is easy to Express*the length of*any of sides of a rectangular**triangle**.