Transcript 9.6 Solving Right Triangles

Examples
• Find the sine, cosine and tangent
of angles A, B.
• Bonus find the sine of angle C.
Sin(A) = 5/13
Sin(B)= 12/13
13
Cos(A)= 12/13 Cos(B)= 5/13
Tan(A)= 5/12
A
12
Tan(B)= 12/5
Sin(C)= 1
B
C
5
Right Triangle Trigonometry
Geometry
Mr. Calise
Ex. 2: Solving a Right Triangle (h)
• Solve the right
triangle. Round
decimals to the
nearest tenth.
g
H
25°
You are looking for
opposite and
13
hypotenuse which is
the sin ratio.
J
h
G
sin H =
opp.
hyp.
h
13 sin 25° =
Set up the correct ratio
13
Substitute values/multiply by reciprocal
13
13(0.4226) ≈ h
5.5 ≈ h
Substitute value from table or calculator
Use your calculator to approximate.
Ex. 2: Solving a Right Triangle (g)
• Solve the right
triangle. Round
decimals to the
nearest tenth.
cos G =
H
g
25°
You are looking for
adjacent and
hypotenuse which is
the cosine ratio.
13
adj.
hyp.
g
13 cos 25° =
13
13(0.9063) ≈ g
11.8 ≈ h
Set up the correct ratio
13
Substitute values/multiply by reciprocal
Substitute value from table or calculator
Use your calculator to approximate.
J
h
G
Using Right Triangles in Real Life
• Space Shuttle: During its
approach to Earth, the
space shuttle’s glide
angle changes.
• A. When the shuttle’s
altitude is about 15.7
miles, its horizontal
distance to the runway is
about 59 miles. What is
its glide angle? Round
your answer to the
nearest tenth.
Solution:
• You know opposite
and adjacent sides. If
you take the opposite
and divide it by the
adjacent sides, then
take the inverse
tangent of the ratio,
this will yield you the
slide angle.
Glide  = x°
altitude
15.7
miles
distance to runway
59 miles
tan x° =
opp.
Use correct ratio
adj.
tan x° =
15.7
Substitute values
59
Key in calculator 2nd function,
tan 15.7/59 ≈ 14.9
 When the space shuttle’s altitude is about 15.7 miles, the
glide angle is about 14.9°.
B. Solution
Glide  = 19°
altitude
h
• When the space
shuttle is 5 miles from
the runway, its glide
angle is about 19°.
Find the shuttle’s
altitude at this point in
its descent. Round
your answer to the
nearest tenth.
distance to runway
5 miles
tan 19° =
opp.
adj.
tan 19° =
h
Substitute values
5
5 tan 19° =
h
5
 The shuttle’s altitude is
about 1.7 miles.
Use correct ratio
5
Isolate h by
multiplying by 5.
1.7 ≈ h Approximate using calculator
Drill: Find the height of the tree.
40o
50 feet