day 19: exploring trigonometric ratios (soh-cah-toa)
DESCRIPTION
Day 19: Exploring Trigonometric Ratios (SOH-CAH-TOA). The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions. SIN E. COS INE. TAN GENT. SIN E. Pronounced “sign”. COS INE. Pronounced “co-sign”. TAN GENT. Pronounced “tan-gent”. - PowerPoint PPT PresentationTRANSCRIPT
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Lesson 15: Trigonometric Ratios
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The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
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The Trigonometric Functions
SINE
COSINE
TANGENT
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SINE
Pronounced “sign”
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Pronounced “co-sign”
COSINE
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Pronounced “tan-gent”
TANGENT
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Prounounced “theta”
Greek Letter
Represents an unknown angle
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oppositehypotenuse
LegOppSin
Hyp
adjacent tan
Opp LegAdj Leg
hypotenuseopposite
adjacent
LegAdjCos
Hyp
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SOH-CAH-TOA
S - SineO - OppositeH – Hypotenuse
C - CosineA – AdjacentH – Hypotenuse
T – TangentO - OppositeA - Adjacent
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Finding sin, cos, and tan.
(Just writing a ratio.)
1. Circle Angle.
2. Label sides (hyp, opp, adj)
3. Set up ratio
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Find the sine, the cosine, and the tangent of angle A.
Give a fraction.
hyp
oppA sin
8.10
9
hyp
adjA cos
8.10
6
adj
oppA tan
6
9 3
2
9
6
10.8
A
Shrink yourself down and stand where the angle is.Now, figure out your ratios.
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Find the sine, the cosine, and the tangent of angle A
A
24.5
23.1
8.2
hyp
oppA sin
5.24
2.8
hyp
adjA cos
5.24
1.23
adj
oppA tan
1.23
2.8
Shrink yourself down and stand where the angle is.Now, figure out your ratios.
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1. Set up and calculate the trig ratios for sine, cosine and tangent of angle A.
2. Set up and calculate the trig ratios for sine, cosine and tangent of angle B.
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A carpenter needs to measure the length of the beams that will support a roof. The building is 50 feet wide. The roof will rise at an angle of 30º from the top of the walls. The peak of the roof is 14.43 feet above the top of the walls. The side adjacent to the 30º angle is half the width of the building. How long is each supporting beam, b, to the nearest thousandths? Add 2 feet to the beam length so that the roof can extend 2 feet past the walls. What is the cosine of 30º?
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A water park has a straight slide into a deep pool. The slide is 50 feet long. It rises from the pool at an angle of 45º. How tall do the vertical supports of the platform need to be to support the platform at the top of the slide? The bottom of the slide is 35.355 feet from the vertical supports. What is the sine of 45º? Round to the nearest thousandths.
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Students are having a contest to see who can find the tallest tree in a park. To win, a student must measure the height of the tree without climbing the tree. Martha locates a very tall oak tree. She measures that the tree’s shadow is 45 feet long. Martha has a shadow that is 11.5 feet long. She is 5.75 feet tall. How tall is the oak tree? What is the tangent of ∠A?
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Lesson 15: Finding Missing Sides and Angles
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Finding an angle.
(Figuring out which ratio to use and an inverse trig
button.)1. Circle Angle.
2. Label sides (hyp, opp, adj)
3. Set up ratio
4. Calculate using inverse trig
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Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.
20 m
40 m
20tan
40
26.6o
1 20tan
40x
Tan-1 20 / 40 )
Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
x
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Ex: 2 Figure out which ratio to use. Find x. Round to the nearest tenth.
15 m50 m 15
sin50
17.5 o
1 15sin
50x
Sin-1 15 / 50 )
Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
x
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Ex. 3: Find . Round to the nearest degree.
9
17.29
2.17tan
62
1 17.2tan
9
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Ex. 4: Find . Round to the nearest degree.
23
7
23
7cos
72
1 7cos
23
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Ex. 5: Find . Round to the nearest degree.
400
200
400
200sin
30
1 200sin
400
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Finding a side.(Figuring out which ratio to use and getting to use a trig
button.)1. Circle Angle.
2. Label sides (hyp, opp, adj)
3. Set up ratio
4. Cross Multiply
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Ex: 6 Figure out which ratio to use. Find x. Round to the nearest tenth.
5520 m
x
20
55tanx
m 6.28x
x55tan20tan 20 55 )
Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
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Ex: 7 Find the missing side. Round to the nearest tenth.
72
80 ft
x
x
8072tan
ft 26x
8072tan x
72tan
80x
tan 80 72 = ( ) )Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.
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Ex: 8 Find the missing side. Round to the nearest tenth.
24
283 mx 283
24sinx
m 1.115x
x24sin283Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
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Ex: 9 Find the missing side. Round to the nearest tenth.
4020 ft x
2040cos
x
ft 3.15x
x40cos20
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When we are trying to find a
side we use sin, cos, or tan.
When we are trying to find an angle we use (INVERSE) sin-1, cos-1, or tan-1.