How do you find out length of sides of a triangle?

Answer 1

The length of a side of a right triangle, a triangle in which one of the interior angles is 90 degrees (a right angle), is found using the Pythagorean Theorem (a^2 + b^2 = c^2) if you know the lengths of the other two sides. The length of the hypotenuse, the side opposite the right angle, is c, and a and b are the lengths of the other two sides. So c is the square root of the sum of the squares of a and b, a is the square root of (c^2 - b^2), and b is the square root of (c^2 - a^2).

For example, if a and b are 3 cm and 4 cm,...

c = (a^2 + b^2)^(1/2) = [(3 cm)^2 + (4 cm)^2]^(1/2) = (9 cm^2 + 16 cm^2)^(1/2)
= (25 cm^2)^(1/2) = [(5 cm)^2]^(1/2) = 5 cm

The hypotenuse, c, is always the longest of the three sides.

If you know the length of only one side but you also know the measure of the other angles, you use the trigonometric functions of sine, cosine or tangent. Angle A is the interior angle opposite side a, and angle B is opposite side b. The sine of an angle is the ratio of the length of the opposite side in a right triangle to the length of the hypotenuse, the cosine is the ratio of the length of the adjacent side to the length of the hypotenuse, and the tangent is the ratio of the length of the opposite side to the length of the adjacent side. The equations look like this:

• sinA = a/c
• sinB = b/c
• cosA = b/c
• cosB = a/c
• tanA = a/b
• tanB = b/a

Multiplying both sides of each equation by the divisor or denominator of the right side yields...

• a = c * sinA
• b = c * sinB
• b = c * cosA
• a = c * cosB
• a = b * tanA
• b = a * tanB

and by dividing both sides of each of these equations by the trig function, we get...

• c = a/sinA
• c = b/sinB
• c = b/cosA
• c = a/cosB
• b = a/tanA
• a = b/tanB

The sum of the interior angles of every triangle is always 180 degrees, so in a right triangle,...

A + B = (180 - 90) degrees = 90 degrees

Therefore,...

A = 90 degrees - B, and
B = 90 degrees - A

It doesn't matter which angle you call A and which is B or which side is a and which is b as long as c, the hypotenuse, is the longest side and opposite the right angle, a is opposite A, and b is opposite B.

If you are working with a triangle that is not a right triangle, you can turn it into two right triangles by drawing an interior line that is perpendicular to one of the sides and that intersects the vertex of the opposite angle.

Answer 2

The answer depends on what information you have about the triangle.