Transcript 9.6 - My Haiku

Agenda 2/25/13
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1) Bell Work
2) Outcomes
3)Finish Solving Right Triangle Notes(9.6)
4) Review quiz concepts
5) Problem Packet(possibly group work)
• tablet password = cosine
Bell Work 2/27/13
• 1)Use Pythagorean Theorem 2) Use Special Right
• x = _____ y = _____
a = _____ b = ____
• 3) Solve for the missing side using Trig Ratios
• A)
B)
• w = _____
x = _____
Outcomes
• I will be able to:
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1) Use Properties of special right triangles
2) Understand Trigonometric Ratios
3) Use Pythagorean Theorem
4) Understand proportions in triangles
9.6 Notes – Solving Right Triangles
• What does it mean to solve a right triangle?
• Solve a Right Triangle – Determine the
measures of all six parts of a right triangle (3
angles and 3 sides).
• You can solve a right triangle if you know:
• 1. Two side lengths
• 2. One side length and one acute angle
measure
Inverses
1
sin x  mA
• 1. If sin A = x, then _________________.
1
•
cos
y

m

A
2. If cos A = y, then _________________.
1
tan x  mA
• 3. If tan A = z, then _________________.
• ***You can use either your calculator or your
trig table to determine the angle measure.
Examples
• Use a calculator or trig ratio table to find the
following.
• 1. Sin A = .9205
2. Cos B = .1392
67
82
• 3. Tan C = 11.4301
85
4. Cos A = .9659
15
Examples
• 5. Solve the right triangle. Round decimals to
the nearest tenth.
• What trig ratios do we have
to determine angle A and C?
C
• From A: Cos A = 8/10 = .8
• From C: Sin C = 8/10 = .8
10
• Look at trig table to
determine the angle measures
B
A
• Angle A = 36°
8
• Angle C = 54°
Examples
• 6. Solve the right triangle. Round decimals to the
nearest tenth.
• What trig ratios do we have?
• Looking at a
a
• Sin 65 = a/20
Y
Z
• Convert Sin 65 to decimal
b
using chart
20
65º
• .9063 = a/20
x
• x 20
x 20
• 18.1 = a
• Cos 65 = b/20 – repeat the process
• .4226 = b/20
• 8.5 = b
Examples
• 7. Solve the right triangle. Round decimals to the
nearest tenth.
S
x
15
20º
T
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What trig ratios do we have?
Cos 20 = y/15
.9397 = y/15
14.1 = y
Sin 20 = x/15
.3420 = x/15
5.1 = x
y
R
Examples
• 8. During a hot air balloon flight, Willie and Nia look upwards
and see the balloon, as shown in the diagram below. The
angle of elevation from Nia is 28˚ and she is 1.8 miles from the
spot on the ground directly below the balloon.
• What is the height of the
• Tan 28° = h/1.8
• h = .96
balloon?
h
28°
W
• Willie is 2.8 miles from Nia.
1
Find the angle of elevation from Willie.
• Tan W = .96/1
• m ∠W = 44°
1.8
N