5-Minute Check on Lesson 7-5

1
Transparency 7-6
5-Minute Check on Lesson 7-5

• Name the angles of depression and elevation in
  the two figures.
• 
  2.
• 3. Find the angle of elevation of the sun when a
  6-meter flag pole casts a 17-meter shadow.
• After flying at an altitude of 575 meters, a
  helicopter starts to descend when its ground
  distance from the landing pad is 13.5 Km. What
  is the angle of depression for this part of the
  flight?
• The top of a signal tower is 250 feet above sea
  level. The angle of depression for the tope of
  the tower to a passing ship is 19. How far is
  the foot of the tower from the ship?
• From a point 50 feet from the base of a tree,
  the angle of elevation to the top of the tree is
  32. From a point closer to the base of the
  tree, the angle of elevation is 64. Which of
  the following is the best estimate of the
  distance between the two points at which the
  angle of elevation is measured?

?FED ?CDE
?URT ?STR
about 19.4
about 2.4
about 726 ft
15
28
29
35
A
C
B
D
D
Click the mouse button or press the Space Bar to
display the answers.
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Lesson 7-6

• Law of Sines

3
Objectives

• Use the Law of Sines to solve triangles
• Solve problems by using the Law of Sines

4
Vocabulary

• Solving a triangle means finding the measures
  of all sides and all angles

5
Law of Sines
A
Let ?ABC be any triangle with a, b and c
representing the measures of the sides opposite
the angles with measures A, B, and C
respectively. Then
b
c
C
B
a
sin A sin B sin
C
a b
c
Law of Sines can be used to find missing parts of
triangles that are not right triangles Case 1
measures of two angles and any side of the
triangle (AAS or ASA) Case 2 measures of two
sides and an angle opposite one of the known
sides of the triangle (SSA)
6
Example 1
Find p. Round to the nearest tenth.
Law of Sines
Cross products
Use a calculator.
7
Example 2
Law of Sines
Cross products
Divide each side by 7.
Solve for L.
Use a calculator.
8
Example 3
a. Find c. b. Find m?T to the nearest
degree in ?RST if r 12, t 7, and m?T 76.
9
Example 4
Angle Sum Theorem
Add.
Subtract 120 from each side.
10
Example 4 cont
To find d
Law of Sines
Substitute.
Cross products
Divide each side by sin 8.
Use a calculator.
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Example 4 cont
To find e
Law of Sines
Substitute.
Cross products
Divide each side by sin 8.
Use a calculator.
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Example 5
We know the measure of two sides and an angle
opposite one of the sides.
Law of Sines
Cross products
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Example 5 cont
Divide each side by 16.
Solve for L.
Use a calculator.
Angle Sum Theorem
Substitute.
Add.
Subtract 116 from each side.
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Example 5 cont
Law of Sines
Cross products
Use a calculator.
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Example 6
16
Example 7
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Example 7 cont
Law of Sines
Cross products
Use a calculator.
Answer The length of the shadow is about 75.9
feet.
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Example 8
A 5-foot fishing pole is anchored to the edge of
a dock. If the distance from the foot of the pole
to the point where the fishing line meets the
water is 45 feet, about how much fishing line
that is cast out is above the surface of the
water?
Answer About 42 feet of the fishing line that
is cast out is above the surface of the water.
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Summary Homework

• Summary
• Law of Sines can be used to solve for angles and
  sides in triangles that are not right triangles
• Case 1 measures of two angles and any side of
  the triangle (AAS or ASA)
• Case 2 measures of two sides and an angle
  opposite one of the known sides of the triangle
  (SSA)
• Homework
• pg 380-381 1, 4-7, 17-21, 30, 32