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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
Heaven BucknerHeaven Buckner
Oct. 26, 2010Oct. 26, 2010
Trig 1Trig 1stst
BlockBlock
Mr. PharesMr. Phares
Sine is used for SOHSine is used for SOH
 If the roof is 18 feetIf the roof is 18 feet
long, at a 35long, at a 35˚ angle.˚ angle.
What is the height ofWhat is the height of
the roof?the roof?
 sin(35)/1= opp/hypsin(35)/1= opp/hyp
 sin(35)/1= x/18sin(35)/1= x/18
 18sin(35)= x18sin(35)= x
 10.32 ft= x10.32 ft= x
 The roof is 10.32 feetThe roof is 10.32 feet
high.high.
35˚
18ft
x
Cosine is used for CAHCosine is used for CAH
 If a street light’s height isIf a street light’s height is
unknown and is shadow isunknown and is shadow is
32 feet long and is at a 6032 feet long and is at a 60˚˚
angle. How tall is the streetangle. How tall is the street
light?light?
 Cos(60)/1= adj/hypCos(60)/1= adj/hyp
 Cos(60)/1=x/32Cos(60)/1=x/32
 32cos(60)=x32cos(60)=x
 16 ft.=x16 ft.=x
 The street light is 16 feetThe street light is 16 feet
tall.tall.
32 ft.
60˚
x
Tangent is used for TOATangent is used for TOA
 If a building is 16 metersIf a building is 16 meters
tall, and it’s shadow is casttall, and it’s shadow is cast
at a 45at a 45˚ angle. How long is˚ angle. How long is
it’s shadow?it’s shadow?
 Tan(45)/1= opp/adjTan(45)/1= opp/adj
 Tan(45)/1= 16/xTan(45)/1= 16/x
 16=xtan(45)16=xtan(45)
 16/tan(45)=xtan(45)/tan(45)16/tan(45)=xtan(45)/tan(45)
 16m=x16m=x
 The building’s shadow isThe building’s shadow is
16 meters long.16 meters long.
x
16m
45˚
SummarySummary
 You can use soh, cah, toa to find multipleYou can use soh, cah, toa to find multiple
things of a right triangle.things of a right triangle.
 They are used to find unknown angles andThey are used to find unknown angles and
unknown sides of a right triangle.unknown sides of a right triangle.
 Soh, cah, toa is perfect for finding the lengthSoh, cah, toa is perfect for finding the length
of a shadow, or the height of a building.of a shadow, or the height of a building.
With the angles you, can find the angle thatWith the angles you, can find the angle that
the shadow is cast from.the shadow is cast from.
SummarySummary
 You can use soh, cah, toa to find multipleYou can use soh, cah, toa to find multiple
things of a right triangle.things of a right triangle.
 They are used to find unknown angles andThey are used to find unknown angles and
unknown sides of a right triangle.unknown sides of a right triangle.
 Soh, cah, toa is perfect for finding the lengthSoh, cah, toa is perfect for finding the length
of a shadow, or the height of a building.of a shadow, or the height of a building.
With the angles you, can find the angle thatWith the angles you, can find the angle that
the shadow is cast from.the shadow is cast from.

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Heaven Buckner

  • 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 Heaven BucknerHeaven Buckner Oct. 26, 2010Oct. 26, 2010 Trig 1Trig 1stst BlockBlock Mr. PharesMr. Phares
  • 2. Sine is used for SOHSine is used for SOH  If the roof is 18 feetIf the roof is 18 feet long, at a 35long, at a 35˚ angle.˚ angle. What is the height ofWhat is the height of the roof?the roof?  sin(35)/1= opp/hypsin(35)/1= opp/hyp  sin(35)/1= x/18sin(35)/1= x/18  18sin(35)= x18sin(35)= x  10.32 ft= x10.32 ft= x  The roof is 10.32 feetThe roof is 10.32 feet high.high. 35˚ 18ft x
  • 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 is shadow isunknown and is shadow is 32 feet long and is at a 6032 feet long and is at a 60˚˚ angle. How tall is the streetangle. How tall is the street light?light?  Cos(60)/1= adj/hypCos(60)/1= adj/hyp  Cos(60)/1=x/32Cos(60)/1=x/32  32cos(60)=x32cos(60)=x  16 ft.=x16 ft.=x  The street light is 16 feetThe street light is 16 feet tall.tall. 32 ft. 60˚ x
  • 4. Tangent is used for TOATangent is used for TOA  If a building is 16 metersIf a building is 16 meters tall, and it’s shadow is casttall, and it’s shadow is cast at a 45at a 45˚ angle. How long is˚ angle. How long is it’s shadow?it’s shadow?  Tan(45)/1= opp/adjTan(45)/1= opp/adj  Tan(45)/1= 16/xTan(45)/1= 16/x  16=xtan(45)16=xtan(45)  16/tan(45)=xtan(45)/tan(45)16/tan(45)=xtan(45)/tan(45)  16m=x16m=x  The building’s shadow isThe building’s shadow is 16 meters long.16 meters long. x 16m 45˚
  • 5. SummarySummary  You can use soh, cah, toa to find multipleYou can use soh, cah, toa to find multiple things of a right triangle.things of a right triangle.  They are used to find unknown angles andThey are used to find unknown angles and unknown sides of a right triangle.unknown sides of a right triangle.  Soh, cah, toa is perfect for finding the lengthSoh, cah, toa is perfect for finding the length of a shadow, or the height of a building.of a shadow, or the height of a building. With the angles you, can find the angle thatWith the angles you, can find the angle that the shadow is cast from.the shadow is cast from.
  • 6. SummarySummary  You can use soh, cah, toa to find multipleYou can use soh, cah, toa to find multiple things of a right triangle.things of a right triangle.  They are used to find unknown angles andThey are used to find unknown angles and unknown sides of a right triangle.unknown sides of a right triangle.  Soh, cah, toa is perfect for finding the lengthSoh, cah, toa is perfect for finding the length of a shadow, or the height of a building.of a shadow, or the height of a building. With the angles you, can find the angle thatWith the angles you, can find the angle that the shadow is cast from.the shadow is cast from.