1. Law of Sines through Applications
Section 6.1A
Precalculus PreAP/Dual, Revised ©2017
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§6.1A: Law of Sines through Applications

2. §6.1A: Law of Sines through Applications
Example 1
Alyssa is taking a walk along a straight road. She decides to leave the road so she walks on a path that makes an angle of 𝟑𝟓° with the road. After walking 𝟒𝟓𝟎 meters, she turns 𝟕𝟓° and heads back towards the road. How far does she need to walk on her current path to get back to the road?
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§6.1A: Law of Sines through Applications

3. §6.1A: Law of Sines through Applications
Example 2
A blimp is seen over Austin, Texas at the same time by 𝟐 observers that are 𝟏𝟐 miles from one another on Congress Street. If the observers are on opposite sides of the blimp and the angles of elevation of the observers to the blimp are 𝟐𝟖° and 𝟑𝟕°, find the height of the blimp. Round to four decimal places.
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§6.1A: Law of Sines through Applications

4. §6.1A: Law of Sines through Applications
Example 2
A blimp is seen over Austin, Texas at the same time by 𝟐 observers that are 𝟏𝟐 miles from one another on Congress Street. If the observers are on opposite sides of the blimp and the angles of elevation of the observers to the blimp are 𝟐𝟖° and 𝟑𝟕°, find the height of the blimp. Round to four decimal places.
2/25/2019 9:30 AM
§6.1A: Law of Sines through Applications

5. §6.1A: Law of Sines through Applications
Your Turn
To measure the height of a mountain, a surveyor takes two sightings of the peak at a distance 900 meters apart on a direct line to the mountain. The first observation results in an angle of elevation of 𝟒𝟕°, and the second results in an angle of elevation of 𝟑𝟓°. If the transit is 2 meters high, what is the height 𝒉 of the mountain?
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§6.1A: Law of Sines through Applications

6. §6.1A: Law of Sines through Applications
Question
Determine the area of this triangle in centimeters
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§6.1A: Law of Sines through Applications

7. §6.1A: Law of Sines through Applications
Question
Determine the area of this triangle in centimeters
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§6.1A: Law of Sines through Applications

8. §6.1A: Law of Sines through Applications
The Area of a Triangle
The area of any triangle is given by 𝑨= 𝟏 𝟐 𝒃𝒉, where 𝒃 is its base and 𝒉 is its height.
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§6.1A: Law of Sines through Applications

9. §6.1A: Law of Sines through Applications
The Area of a Triangle
The area of any triangle is given by 𝑨= 𝟏 𝟐 𝒃𝒉, where 𝒃 is its base and 𝒉 is its height.
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§6.1A: Law of Sines through Applications

10. Steps in Solving Area of a Triangle
Use this method in SAS Triangles
Draw a picture of triangle
Plug into the equation, 𝑨= 𝟏 𝟐 𝒂𝒄 𝐬𝐢𝐧⁡𝑩
The calculator is in degree mode
Round to four decimal places
Label appropriately
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§6.1A: Law of Sines through Applications

11. §6.1A: Law of Sines through Applications
Example 3
The area of triangle 𝑨𝑩𝑪 if 𝑩=𝟓𝟓°, 𝒂=𝟑𝟒 feet, and 𝒄=𝟒𝟐 feet.
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§6.1A: Law of Sines through Applications

12. §6.1A: Law of Sines through Applications
Example 4
The area of triangle 𝑨𝑩𝑪 if 𝒂=𝟏𝟎 feet, 𝒃=𝟔 feet, and 𝑨=𝟒𝟐°
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§6.1A: Law of Sines through Applications

13. §6.1A: Law of Sines through Applications
Example 4
The area of triangle 𝑨𝑩𝑪 if 𝒂=𝟏𝟎 feet, 𝒃=𝟔 feet, and 𝑨=𝟒𝟐°
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§6.1A: Law of Sines through Applications

14. §6.1A: Law of Sines through Applications
Your Turn
The area of triangle 𝑨𝑩𝑪 if 𝑩=𝟐𝟕°, 𝒂=𝟒 𝒎., and 𝒃= 𝟖 𝒎.
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§6.1A: Law of Sines through Applications

15. §6.1A: Law of Sines through Applications
Assignment
Page odd (omit 41)
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§6.1A: Law of Sines through Applications