5.02 Trig Ratios Day 1 - Math 2

Right Triangle Trigonometry

Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles. It focuses on calculations involving triangles, especially right-angled triangles, using trigonometric functions like sine, cosine, and tangent to find unknown angles or side lengths. The word "trigonometry" comes from Greek words for "triangle" (trigonon) and "measure" (metron). 

Sides of a Right Triangle

• The HYPOTENUSE is directly across from the right angle.

• The OPPOSITE side is directly across from the referenced angle.

• The ADJACENT side is the last side. It is the side that touches the angle, but isn't the hypotenuse.

The Angle

The referenced angle could be indicated by the Greek symbol "theta", by an arc marking it, or by a measure placed in the figure. It could also be marked with an "x" or other variable if you're expected to use trig to find its measure.

Multiple Choice

In relation to the angle θ, label the side marked a in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked b in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked c in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked c in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked b in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

In relation to the angle θ, label the side marked b in this right-angled triangle.

• Hypotenuse

• Adjacent

• Opposite

Multiple Choice

The hypotenuse is always across from the right angle of a triangle.

• False

• True

Multiple Choice

Which side of the triangle is adjacent to angle R?

• QP

• QR

• RP

Multiple Choice

Which side of the triangle is the hypotenuse?

• QP

• QR

• RP

Multiple Choice

Which side of the triangle is opposite of angle R?

• QP

• QR

• RP

Trigonometric Ratios

The ratios formed by the side lengths of a right triangle.

*We use these to solve for missing sides and/or missing angles of right triangles.

sine (sin)

cosine (cos)

The cosine of an angle is the ratio of the length of the side ADJACENT to the reference angle to the length of the HYPOTENUSE.

tangent (tan)

The tangent is the ratio of the side OPPOSITE the reference angle over the length of the side ADJACENT to the reference angle.

How Will I Remember All of Those Ratios?????

Here's How!

Multiple Choice

What is a common way to remember the definitions of the trig ratios?

• SAH COH TOA

• SOA COH TOA

• SOH CAH TOA

• ADJ OPP HYP

Multiple Choice

Which is the correct ratio for the sine ratio?

• $$\frac{adjacent\ }{hypotenuse}$$

• $$\frac{opposite\ }{hypotenuse}$$

• $$\frac{adjacent\ }{opposite\ }$$

• $$\frac{opposite\ }{adjacent\ }$$

Multiple Choice

Which is the correct ratio for the tangent ratio?

• $$\frac{adjacent\ }{hypotenuse}$$

• $$\frac{opposite\ }{hypotenuse}$$

• $$\frac{adjacent\ }{opposite\ }$$

• $$\frac{opposite\ }{adjacent\ }$$

Multiple Choice

Which is the correct ratio for the cosine ratio?

• $$\frac{adjacent\ }{hypotenuse}$$

• $$\frac{opposite\ }{hypotenuse}$$

• $$\frac{adjacent\ }{opposite\ }$$

• $$\frac{opposite\ }{adjacent\ }$$

Multiple Choice

Which ratio represents

$$\cos\left(\angle W\right)$$  ?

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

Which ratio represents

$$\tan\left(\angle W\right)$$  ?

• $$\frac{8}{17}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{15}$$  

Multiple Choice

Which ratio represents

$$\sin\left(\angle S\right)$$  ?

• $$\frac{20}{29}$$  

• $$\frac{21}{20}$$  

• $$\frac{21}{29}$$  

Multiple Choice

What is the correct trigonometric ratio for the sine of A?

Multiple Choice

What is the correct trigonometric ratio for the cosine of B?

Multiple Choice

What is the correct trigonometric ratio for the tangent of A?

Multiple Choice

What is the correct trigonometric ratio for the sine of B?

Multiple Choice

Write the correct Trig proportion

• sin 20 = $$\frac{14}{x}$$

• cos 20 = $$\frac{14}{x}$$

• tan 20 = $$\frac{14}{x}$$

• tan 20 = $$\frac{x}{14}$$

Multiple Choice

Write the correct Trig proportion

• sin 20 = $$\frac{14}{x}$$

• cos 20 = undefined

• tan 20 = undefined

• sin 20 = $$\frac{x}{14}$$

Multiple Choice

Find the correct proportion:

• sin 64 = $$\frac{13}{x}$$

• tan 64 = $$\frac{13}{x}$$

• tan 64 = $$\frac{x}{13}$$

• sin 64 = $$\frac{x}{13}$$

Multiple Choice

Find the correct proportion:

• sin 64 = $$\frac{13}{x}$$

• cos 64 = undefined

• tan 64 = undefined

• tan 64 = $$\frac{x}{13}$$

• cos 64 = $$\frac{x}{13}$$

Multiple Choice

Find the correct proportion:

• sin 64 = $$\frac{13}{x}$$

• cos 64 = $$\frac{13}{x}$$

• tan 64 = $$\frac{13}{x}$$

• tan 64 = $$\frac{x}{13}$$

• sin 64 = $$\frac{x}{13}$$

Multiple Choice

Which equation can be used to find the value of x?

• sin(52) = $$\frac{21}{x}$$

• tan(52) = $$\frac{21}{x}$$

• sin(52) = $$\frac{x}{21}$$

• tan(52) = $$\frac{x}{21}$$

• cos(52)= $$\frac{21}{x}$$

Multiple Choice

Which equation can be used to find the value of x?

• cos(71) = $$\frac{x}{15}$$

• cos(71) = $$\frac{15}{x}$$

• sin(71) = $$\frac{x}{15}$$

• sin(71) = $$\frac{15}{x}$$

• tan(71)= $$\frac{x}{15}$$

Multiple Choice

Which trig function would you use to solve for x?

• 
  

  $$\sin\ 17\ =\frac{x}{15}$$
  

• $$\cos\ 17\ =\frac{x}{15}$$

• $$\tan\ 17=\frac{x}{15}$$

• $$\cos\ 17=\frac{15}{x}$$

Multiple Choice

Which is the correct set up to solve for x?

• sin 24 = x / 12
• cos 24 = x / 12
• tan 24 = x / 12

Mixed Review

Multiple Choice

Give the Ratio for SIN X

• opp/adj
• Adj/hyp
• Opp/hyp
  
• adj/opp

Multiple Choice

If you are given the hypotenuse and an adjacent side, which trig function should you use?

• sine
• cosine
• tangent
• cotangent

Multiple Choice

Give the Ratio for COS X

• Adj/Hyp
• Opp/Adj
• Adj/Opp
• Opp/Hyp

Multiple Choice

Which one is the easy trick to remember trigonometric ratios?

• Sah Coh Toa
• Soh Cah Toa
• Soh Cah Tao
• Soh Ceh Toa

Multiple Choice

Set up the problem...

• sin X = 41/28
• tan X = 41/28
• cos X = 28/41
• sin X = 28/41

Multiple Choice

Give the Ratio for TAN X

• Adj/Opp
• Opp/Adj
• Adj/Hyp
• Opp/Hyp

Multiple Choice

Choose the correct ratio.

• $$\sin Z=\frac{5}{13}$$

• $$\cos\ Z\ =\ \frac{5}{13}$$

• $$\tan Z=\frac{5}{13}$$

Multiple Choice

Which is the correct set up to solve for x?

• sin 37 = x / 12
• cos 37 = 12 / x
• tan 37 = x / 12
• sin 37 = 12 / x

Multiple Choice

What side is adjacent to $$\angle$$ J?  

• 9

• 40

• 41

• none

The End