Right Triangle Geometry

“for physics students”

Right Triangles

• Right triangles are triangles in which one of the interior angles is 90o – A 90o angle is called a right angle. – The other two interior angles are

complementary, i.e. their sum equals 90o.

Anatomy of a Right Triangle

• The side opposite of the right angle is called the hypotenuse.

• The sides adjacent to the right angle are the legs. – c – hypotenuse– a & b – the other two legs

The Pythagorean theorem• The Pythagorean Theorem states that:

– In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two

sides. – Using the Pythagorean Theorem,

if the lengths of any two of the

sides of a right triangle are known

and it is known which side is the

hypotenuse, then the length of the

third side can be determined from

the formula.

Sine, Cosine & Tangent Functions

• Sine, Cosine, and Tangent are all functions of an angle, which are useful in right triangle calculations.

• For an angle designated as θ, the sine function is abbreviated as sin θ, the cosine function is abbreviated as cos θ, and the tangent function is abbreviated as tan θ.

• In a right triangle,– the sine of a non-right angle equals the length of the leg

opposite that angle divided by the length of the hypotenuse. – the cosine of a non-right angle equals the length of the leg

adjacent to it divided by the length of the hypotenuse. – the tangent of a non-right angle equals the length of the leg

opposite that angle divided by the length of the leg adjacent to it.

SOH CAH TOA

S – sineO – oppositeH – hypotenuseC – cosineA – adjacentH – hypotenuseT – tangentO – oppositeA – adjacent

• Neat website

Now you try.1. What would a be if b were 34 N and c

were 60 N?

2. What would b be if ϴ2 were 30° and a was 50 N?

3. If ϴ1 was 55° and c was 100 N what would a and b be?