Download Right Triangle Geometry

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 – sine
O – opposite
H – hypotenuse
C – cosine
A – adjacent
H – hypotenuse
T – tangent
O – opposite
A – 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?