Trig Ratios, Sides, and Angles

What is the definition of a right triangle?

• A triangle with all angles measuring less than 90 degrees.

• A triangle that has one angle measuring 90 degrees.

• A triangle with two equal sides and one angle measuring 60 degrees.

• A triangle that has three sides of different lengths.

What is the cosine ratio?

• The ratio of the length of the opposite side to the length of the hypotenuse: @@ ext{sin} = rac{ ext{opposite}}{ ext{hypotenuse}}@@

• The ratio of the length of the adjacent side to the length of the hypotenuse: @@ ext{cosine} = rac{ ext{adjacent}}{ ext{hypotenuse}}@@

• The ratio of the length of the adjacent side to the length of the opposite side: @@ ext{tan} = rac{ ext{adjacent}}{ ext{opposite}}@@

• The ratio of the length of the hypotenuse to the length of the opposite side: @@ ext{cosec} = rac{ ext{hypotenuse}}{ ext{opposite}}@@

What is the relationship between the angles in a right triangle?

• The sum of the angles is always 180 degrees, with one angle being 90 degrees.

• The sum of the angles is always 90 degrees, with one angle being 45 degrees.

• The sum of the angles is always 360 degrees, with one angle being 90 degrees.

• The sum of the angles is always 180 degrees, with all angles being acute.

How do you find the measure of an angle using the cosine ratio?

• Use the sine function: @@ heta = ext{sin}^{-1}igg(rac{ ext{opposite}}{ ext{hypotenuse}}igg)@@

• Use the tangent function: @@ heta = ext{tan}^{-1}igg(rac{ ext{opposite}}{ ext{adjacent}}igg)@@

• Use the inverse cosine function: @@ heta = ext{cos}^{-1}igg(rac{ ext{adjacent}}{ ext{hypotenuse}}igg)@@

• Use the Pythagorean theorem to find the angle.

What is the hypotenuse in a triangle with sides 9 and 40?

• 39

• 40

• 41

• 42

If the opposite side is 20 and the adjacent side is 15, what is the tangent ratio?

• @@rac{20}{15} = rac{4}{3}@@

• @@rac{15}{20} = rac{3}{4}@@

• @@rac{20}{20} = 1@@

• @@rac{15}{15} = 1@@

What is the sine of a 30-degree angle?

• @@rac{1}{2}@@

• @@rac{ ext{sqrt}(3)}{2}@@

• @@1@@

• @@0@@

What are the three sides of a right triangle called?

• Hypotenuse, Opposite side, Adjacent side

• Base, Height, Diagonal

• Long side, Short side, Right side

• Vertical side, Horizontal side, Slant side

What is the Pythagorean theorem?

• In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): @@c^2 = a^2 + b^2@@.

• The sum of the lengths of the two shorter sides of a triangle is equal to the length of the longest side.

• In any triangle, the area can be calculated using the formula: Area = 1/2 * base * height.

• The ratio of the lengths of the sides of a triangle is always equal to 1.

How do you find the measure of an angle using the tangent ratio?

• Use the sine function: @@ heta = ext{sin}^{-1}igg(rac{ ext{opposite}}{ ext{hypotenuse}}igg)@@

• Use the cosine function: @@ heta = ext{cos}^{-1}igg(rac{ ext{adjacent}}{ ext{hypotenuse}}igg)@@

• Use the inverse tangent function: @@ heta = ext{tan}^{-1}igg(rac{ ext{opposite}}{ ext{adjacent}}igg)@@

• Use the secant function: @@ heta = ext{sec}^{-1}igg(rac{ ext{hypotenuse}}{ ext{adjacent}}igg)@@