Transcript Document

Transparency 7-6
5-Minute Check on Lesson 7-5
Name the angles of depression and elevation in the two figures.
E
F
FED; CDE
1. R
U
URT; STR 2.
S
T
D
A
C
B
3. Find the angle of elevation of the sun when a 6-meter flag pole casts a 17meter shadow.
about 19.4°
4. 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?
about 2.4°
5. 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?
about 726 ft
6. 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?
15
28
29
35
A
B
C
D
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Lesson 7-6
Law of Sines
Objectives
• Use the Law of Sines to solve triangles
• Solve problems by using the Law of Sines
Vocabulary
• Solving a triangle – means finding the
measures of all sides and all angles
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
sin A
––––––
a
=
sin B
––––––
b
b
c
=
a
sin C
––––––
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)
C
Example 1
Find p. Round to the nearest tenth.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer:
Example 2
to the nearest degree in
,
Law of Sines
Cross products
Divide each side by 7.
Solve for L.
Use a calculator.
Answer:
Example 3
a. Find c.
Answer:
b. Find mT to the nearest degree in RST if r = 12,
t = 7, and mT = 76.
Answer:
Example 4
. Round
angle measures to the nearest degree and side
measures to the nearest tenth.
We know the measures of two angles of the triangle. Use
the Angle Sum Theorem to find
Angle Sum Theorem
Add.
Subtract 120 from each side.
Example 4 cont
To find d:
Law of Sines
Substitute.
Cross products
Divide each side by sin 8°.
Use a calculator.
Example 4 cont
To find e:
Law of Sines
Substitute.
Cross products
Divide each side by sin 8°.
Use a calculator.
Answer:
Example 5
Round angle
measures to the nearest degree and side measures
to the nearest tenth.
We know the measure of two sides and an angle opposite
one of the sides.
Law of Sines
Cross products
Example 5 cont
Divide each side by 16.
Solve for L.
Use a calculator.
Angle Sum Theorem
Substitute.
Add.
Subtract 116 from each side.
Example 5 cont
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer:
Example 6
a. Solve
Round
angle measures to the nearest degree and side
measures to the nearest tenth.
Answer:
b.
Round angle
measures to the nearest degree and side measures to
the nearest tenth.
Answer:
Example 7
A 46-foot telephone pole tilted at an angle of from
the vertical casts a shadow on the ground. Find the
length of the shadow to the nearest foot when the
angle of elevation to the sun is
Draw a diagram Draw
Then find the
Example 7 cont
Since you know the measures of two angles of the
triangle,
and the length of a side
opposite one of the angles
you
can use the Law of Sines to find the length of the shadow.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer: The length of the shadow is about 75.9 feet.
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.
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