Download Learning Target: (LT-7) Solve problems involving special right

Geometry Chapter 5 Lesson 8 – Applying Special Right Triangles
Learning Target: (LT-7) Solve problems involving special right triangles.
Ex1: Find missing sides in 45º-45º-90º Triangles
Find the value of x. Give your answer in simplest radical form.
a.
b.
d.
e.
c.
f.
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Ex2: Find missing sides in 30º- 60º - 90º Triangles
Find the values of x and y. Give your answers in simplest radical form.
a.
b.
c.
d.
e.
f.
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Chapter 8 Trigonometric Ratios
Lesson 8.1 Similarity in Right Triangles
Learning Target: (LT-1) Apply similarity relationships, including the geometric mean, in right
triangles to solve problems.
Geometric Mean:
1. Write a similarity statement comparing the three
triangles.
2. Find the geometric mean of each pair of numbers. If
necessary, give the answer in simplest radical form.
A. 4 and 25
B. 5 and 30
C. 8 and 9
3. Find x, y, and z.
4. To estimate the height of a Douglas fir, Jan positions
herself so that her line of sight to the top and bottom of the
tree form a 90°angle. Her eyes are about 1.6m above the
ground, and she is standing
7.8m from the tree. What
is the height of the tree to
the nearest meter?
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Lesson 8.2 Trigonometric Ratios
Learning Target: (LT-2) Use trigonometric ratios of right triangles to find unknown lengths.
•
trigonometric ratio:
By the AA Similarity Theorem, a right triangle with a given acute angle is similar to every other right
triangle with that same acute angle measure.
Examples:
1. Write each trigonometric ratio as a fraction and a decimal 2. Use a special right triangle to write cos 30° as a fraction.
rounded to the nearest hundredth.
A. sin J
B. cos J
C. tan K
3. Use a special right triangle to
write sin 60° as a fraction.
4. Use your calculator to find each trigonometric ratio,
Round to the nearest hundredth.
A. sin 52°
B. cos 19°
C. tan 65°
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4. Find each length. Round to the nearest hundredth.
A. BC
5. The Pilatusbahn in Switzerland is the world's steepest
cog railway. Its steepest section makes an angle of about
25.6° with the horizontal and rises about 0.9 km. To the
nearest hundredth of a kilometer, how long is this section of
the railway track?
B. QR
C. FD
Ex6. Use special triangles to complete the chart. Answers must be exact values in simplified
radical form.
30º
45º
60º
sin
cos
tan
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Lesson 8.3 – Solving Right Triangles
Learning Target: (LT-3) Use inverse trigonometric ratios of right triangles to find unknown
angles.
Solving a triangle –
Examples:
1. Use the trigonometric ratio cosA =
24
25
to determine
which angle of the triangle is ∠A.
2. Use your calculator to find each angle measure to the
nearest degree.
A. cos-1 (0.87)
B. sin-1 (0.85)
C. tan-1 (0.71)
3. Solve the triangle. Round lengths to the nearest
hundredth and angle measures to the nearest degree.
4. A highway sign warns that a section of road ahead has a
7% grade. To the nearest degree, what angle does the road
make with a horizontal line?
5. The coordinates of the vertices of ΔPQR are P(-3, 3), Q(2, 3), and R(-3, -4). Find the side lengths to the nearest
hundredth and the angle measures to the nearest degree.
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Lesson 8-4 Angles of Elevation and Depression
Learning Target: (LT-4) Solve problems involving angles of depression and angles of elevation.
Angle of elevation –
Angle of depression –
Examples:
1. Classify each angle as an angle of elevation or an angle
of depression.
2. The seattle Space Needle casts
a 67ft. shadow. If the angle of elevation
from the tip of the shadow to the
top of the Space Needle is 70°,
how tall is the Space Needle?
Round to the nearest meter.
3. An ice climber stands at the edge of a crevasse that is
115ft. wide. The angle of depression from the edge where
she stands to the bottom of the opposite side is 52°.
How deep is the
crevasse at this
point? Round to
the nearest foot.
4. What if…? Suppose the ranger sees another fire and the
angle of depression to the fire is 3°. What is the horizontal
distance to this fire? Round to the nearest foot.
5. 4. An observer in a lighthouse is 69ft. above the water. He sights two boats in the water directly in front of him. The
angle of depression to the nearest boat is 48°. The angle of depression to the other boat is 22°. What is the distance
between the two boats? Round to the nearest foot.
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Lesson 8.5 – Law of Sines and Cosines
Learning Target: (LT-5a) Use the Law of Sines to solve problems.
Examples Using The Law of Sines
#1. Use a calculator to find each trigonometric ratio. Round to the nearest hundredth.
A.
tan 103°
B. cos 165°
C. sin 93°
#2. Find each measure. Round lengths to the nearest tenth and angle measures to the nearest
degree.
A.
FG
B.
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m ∠Q
Learning Target: (LT-5b) Use the Law of Cosines to solve problems.
Examples Using The Law of Cosines
Ex#3: Find each measure. Round lengths to the nearest tenth and angle measures to the nearest
degree.
B. m ∠T
A. XZ
Ex#4: A sailing club has planned a triangular racecourse, as shown in the diagram. How long is the
leg of the race along BC ? How many degrees must competitors turn at point C? Round the length
to the nearest tenth and the angle measure to the nearest degree.
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Lesson 8.6 – Vectors
Learning Target: (LT-6) Use vectors to solve problems.
Vocabulary
• vector –
•
component form –
•
magnitude-
•
direction –
•
equal vectors –
•
parallel vectors –
•
resultant vector –
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Examples:
2. Draw the vector 〈−1, 5〉 on a coordinate plane. Find
its magnitude to the nearest tenth.
1. Write each vector in component form.
A.

HG
B.

MN
with M(-8, 1) and N(2, -7).
3, The force exerted by a skier is given by the vector
〈1, 4〉 . Draw the vector on a coordinate plane. Find
the direction of the vector to the nearest degree.
4. Identify each of the following.
A equal vectors.
B. parallel vectors.
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Lesson
Problems
5.8 p. 360
#1-8, 17, 18 & Special Triangles Worksheet
8.1 p. 521
#15-39, 42, 47-49, 54, 57-59
8.2 p. 529
#22-50, 53, 54, 62, 68, 70, 84-86
8.3 p. 538
#21-29, 33, 34, 36, 39-44, 48, 52, 65-67
8.4 p. 547
#10-14, 17-22, 23
8.5 p. 555
Law of Sines
#23-28, 30, 39, 47, 49, 60, 61, 68-74
8.5 p. 555
Law of Cosines
#32-35, 38, 40, 44-46, 51-54, 59
8.6 p. 564
#18-35, 38, 39, 46, 47, 53, 54, 60, 63
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