Triangle Side Lengths and Types

Finding the Length of the Third Side of a Triangle

• To find the length of the third side, write the answer in simplest radical form if necessary.

Pythagorean Theorem and Triangle Types

• If the square of the longest side of a triangle is greater than the sum of the squares of the other two sides, then the triangle is obtuse.
• If the square of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is right.
• If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is acute.

Isosceles Triangles

• An isosceles triangle has two sides of equal length.

Finding Side Lengths with Rational Denominators

• You must express the answer in simplest radical form with a rational denominator.

Trigonometric Ratios

• The formulas depend on the angle given in the problem
• Use the mnemonic SOH CAH TOA to remember the functions
• Sine = Opposite / Hypotenuse
• Cosine = Adjacent / Hypotenuse
• Tangent = Opposite / Adjacent

Solving for Angles

• For angle problems, round answers to the nearest tenth of a degree if necessary.

Real-World Problems Involving Angles of Elevation and Depression

• Angle of Elevation: The angle from the horizontal upwards to an object.
• Angle of Depression: The angle from the horizontal downwards to an object.
• Round answers to the nearest tenth of a foot if necessary.