What to do with Right Triangle Ratios

So far you have learned to write the three trigonometry ratios (comparisons) for the sides of a right triangle. We are now going to use these to solve for some missing information.

Sine Ratio (SIN) is Opposite Leg (of acute angle)

Hypotenuse

Cosine Ratio (COS) is Adjacent Leg (to acute angle)

Hypotenuse

Tangent Ratio (TAN) is Opposite Leg

Adjacent Leg

  1. When you write the ratios for the sides of the right triangles, you are writing the value of the SIN function, COS function, or TAN function of the angle. Use the triangle below to answer the following questions. * The angle, 53.13 has been rounded.

Write the SIN ratio: opp ______now make this ratio a decimal______

hyp

Use your calculator to find the value of the Sine of 53.13˚ (Input 53.13 into the Sine function rule already programed into your calculator.)

Type: SIN key then 53.13 – Enter ______

What do you notice about your two decimals?

Write the COS ratio: Adj ______now make this ratio a decimal ______

Hyp

Use your calculator to find the value of the Cosine of 53.13˚ (input 53.13 into the Cosine function rule already programed into your calculator). Type: COS key then 53.13 – Enter ______

What do you notice about your two decimals?

Write the TAN ratio: Opp ______now make this ratio a decimal ______

Adj

Use your calculator to find the value of the Tangent of 53.13˚(Input 53.13 into the Tangent Function rule already

programed into your calculator). Type: TAN key then 53.13 – Enter ______

What do you notice about your two decimals?

  1. Let’s examine your calculator a little further. There are actually six trig function keys on your calculator. The Sine, Cosine and Tangent keys – SIN, COS, TAN. There are also three more known as the inverse of Sine, the inverse of Cosine, and the Inverse of Tangent. SIN -1, COS -1 and TAN-1. Find these keys now. Where are they located?
  1. Using these keys, find the value of the following functions.

Sin 30 = ______Cos 45 = ______Tan 23 = ______

Sin-1 0.5 = ______Cos-1 0.7071= ______Tan-1 0.424475 = ______

  1. What is the relationship between each trig function and its inverse function? Example SIN and SIN-1
  1. Let’s look at another example.

Write the following ratios: Sin x = ______Cos x = ______Tan x = ______

Brainstorm some ideas about how to use one or more of these ratios plus your calculator to figure out the measure of x.

What is the measure of angle x?

  1. Let’s look at a new example:

Write the following ratios: Sin x = ______Cos x = ______Tan x = ______

Use one or more of these ratios, plus your calculator, to find the value of the missing angle.

What is the measure of the other acute angle that is not marked?

  1. So let’s look back at the examples you worked previously Write the name of the ratio beside each - example Sin, Cos, Tan. Then use one of these ratios to find the measure of the acute angle. Not drawn to scale

.

Ex. Sin α is Opp. Leg= ______α is Opp. Leg= ______α is Opp. Leg = ______

Hypotenuse Hypotenuse Hypotenuse

_____ α is Adj. Leg = ______α Is Adj. Leg = ______α is Adj. Leg = ______

Hypotenuse Hypotenuse Hypotenuse

______α is Opp. Leg= ______α is Opp. Leg = ______α is Opp. Leg = ______

Adj. Leg Adj. Leg Adj. Leg

Angle α = ______α = ______α = ______

  1. Write the given ratio values and then solve for the missing angle measure (α)

Sin α= ______Sin α = ______Sin α = ______

Cos α= ______Cos α = ______Cos α = ______

Tan α = ______Tan α = ______Tan α= ______

Angle α = ______Angle α = ______Angle α = ______

Sin α= ______Sin α = ______

Cos α= ______Cos α = ______

Tan α = ______Tan α = ______

Angle α = ______Angle α = ______