Basic Trig Ratios

How can you find the length of the adjacent side if you know the opposite side and the hypotenuse?

• Use the Pythagorean theorem: Adjacent = @@ ext{Hypotenuse}^2 - ext{Opposite}^2@@.

• Adjacent = @@ ext{Hypotenuse} - ext{Opposite}@@.

• Adjacent = @@ ext{Hypotenuse} imes ext{Opposite}@@.

• Adjacent = @@rac{ ext{Opposite}}{ ext{Hypotenuse}}@@.

What does SOH CAH TOA stand for?

• SOH: Sine = Opposite/Hypotenuse, CAH: Cosine = Adjacent/Hypotenuse, TOA: Tangent = Opposite/Adjacent.

• SOH: Sine = Adjacent/Hypotenuse, CAH: Cosine = Opposite/Hypotenuse, TOA: Tangent = Opposite/Adjacent.

• SOH: Sine = Opposite/Adjacent, CAH: Cosine = Opposite/Hypotenuse, TOA: Tangent = Adjacent/Hypotenuse.

• SOH: Sine = Opposite/Hypotenuse, CAH: Cosine = Opposite/Adjacent, TOA: Tangent = Adjacent/Hypotenuse.

What is the sine of an angle if the opposite side is 5 and the hypotenuse is 13?

• @@rac{5}{13}@@

• @@rac{3}{13}@@

• @@rac{5}{12}@@

• @@rac{12}{13}@@

If the opposite side is 12 and the adjacent side is 16, what is tan(θ)?

• 0.5

• 0.75

• 1.25

• 1.5

What is the tangent of an angle in a right triangle?

• Tangent = Opposite/Adjacent.

• Tangent = Adjacent/Opposite.

• Tangent = Hypotenuse/Opposite.

• Tangent = Opposite + Adjacent.

What is the relationship between the sides of a right triangle?

• The square of the hypotenuse equals the sum of the squares of the other two sides (Pythagorean theorem).

• The sum of the lengths of the two shorter sides equals the length of the hypotenuse.

• The hypotenuse is always the longest side, but its length is not related to the other sides.

• The area of the triangle is equal to the sum of the areas of the two shorter sides.

What is the cosine of an angle if the adjacent side is 30 and the hypotenuse is 50?

• 0.3

• 0.5

• 0.6

• 0.8

What is the value of cos(θ) if the adjacent side is 40 and the hypotenuse is 50?

• 0.6

• 0.7

• 0.8

• 0.9

If the opposite side is 9 and the hypotenuse is 41, what is sin(θ)?

• @@\frac{9}{41}@@

• @@\frac{9}{40}@@

• @@\frac{8}{41}@@

• @@\frac{10}{41}@@

What are the basic trigonometric ratios?

• Sine (sin), Cosine (cos), Tangent (tan)

• Secant (sec), Cosecant (csc), Cotangent (cot)

• Sine (sin), Cosine (cos), Exponential (exp)

• Tangent (tan), Logarithm (log), Sine (sin)