1. How To Use soh, cah, toa ToHow To Use soh, cah, toa To
Solve The Unknowns of a 90Solve The Unknowns of a 90˚˚
TriangleTriangle
Hannah J. BurkeHannah J. Burke
Oct. 26, 2010Oct. 26, 2010
11stst
Block TrigBlock Trig
Mr. PharesMr. Phares

2. Sine is used for SOHSine is used for SOH
 If the roof is 22 feetIf the roof is 22 feet
long, at a 45long, at a 45˚ angle.˚ angle.
What is the height of theWhat is the height of the
roof?roof?
 sin(45)/1= opp/hypsin(45)/1= opp/hyp
 Sin(45)/1= x/22Sin(45)/1= x/22
 22sin(45)= x22sin(45)= x
 15.60 ft= x15.60 ft= x
 The roof is 15.60 feetThe roof is 15.60 feet
high.high.
4545˚˚
22ft22ft
xx

3. Cosine is used for CAHCosine is used for CAH
 If a street light’s height isIf a street light’s height is
unknown and the shadow isunknown and the shadow is
45ft. Long and is at a45ft. Long and is at a
3535˚angle. How tall is the˚angle. How tall is the
street light?street light?
 Cos(35)/1= adj/hypCos(35)/1= adj/hyp
 Cos(35)/1= x/45Cos(35)/1= x/45
 45cos(35)=x45cos(35)=x
 36.9ft=x36.9ft=x
 The street light is 36.9 feetThe street light is 36.9 feet
tall.tall.
45ft.
35˚
x

4. Tangent is used for TOATangent is used for TOA
 A house is 20 meters tall,A house is 20 meters tall,
and the width is unknown.and the width is unknown.
How would you find theHow would you find the
width with a 55width with a 55˚ angle?˚ angle?
 Tan(55)/1=opp/adjTan(55)/1=opp/adj
 Tan(55)/1=20/xTan(55)/1=20/x
 20=x tan(55)20=x tan(55)
 20/tan(55)=x20/tan(55)=x
tan(55)/tan(55)tan(55)/tan(55)
 14m=x14m=x
 The width of the house is 14The width of the house is 14
meters wide.meters wide.
x
20m
55˚

5. SummarySummary
 You use soh, cah, toa to find many different sides of a triangle. TheyYou use soh, cah, toa to find many different sides of a triangle. They
are used to find unknown angles and unknown sides of a right triangle.are used to find unknown angles and unknown sides of a right triangle.
You use them when you are looking for the width of a building or howYou use them when you are looking for the width of a building or how
long a shadow is cast from a certain object. You also can determine thelong a shadow is cast from a certain object. You also can determine the
length of a building or an object by using simple formulas with theselength of a building or an object by using simple formulas with these
terms. It also solves many other things like, distance and other things.terms. It also solves many other things like, distance and other things.

6. SummarySummary
 You use soh, cah, toa to find many different sides of a triangle. TheyYou use soh, cah, toa to find many different sides of a triangle. They
are used to find unknown angles and unknown sides of a right triangle.are used to find unknown angles and unknown sides of a right triangle.
You use them when you are looking for the width of a building or howYou use them when you are looking for the width of a building or how
long a shadow is cast from a certain object. You also can determine thelong a shadow is cast from a certain object. You also can determine the
length of a building or an object by using simple formulas with theselength of a building or an object by using simple formulas with these
terms. It also solves many other things like, distance and other things.terms. It also solves many other things like, distance and other things.