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Law of Sines Skill 42.

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Presentation on theme: "Law of Sines Skill 42."β€” Presentation transcript:

1 Law of Sines Skill 42

2 Objective HSG-SRT.7/8: Students are responsible for using the law of Sines in problems.

3 Law of Sines b B 𝒂 c A C π’”π’Šπ’ 𝑨 𝒂 = π’”π’Šπ’ 𝑩 𝒃 = π’”π’Šπ’ π‘ͺ 𝒄

4 Example 1; Using the Law of Sines (AAS)
a) In βˆ†π΄π΅πΆ, π‘šβˆ π΄=48, π‘šβˆ π΅=93, and 𝐴𝐢=15, find 𝐡𝐢. A B C π’”π’Šπ’ 𝑩 𝒃 = π’”π’Šπ’ 𝑨 𝒂 πŸ’πŸ–Β° π’”π’Šπ’ πŸ—πŸ‘ πŸπŸ“ = π’”π’Šπ’ πŸ’πŸ– 𝒂 πŸπŸ“ π’‚βˆ—π’”π’Šπ’ πŸ—πŸ‘ =πŸπŸ“βˆ—π’”π’Šπ’ πŸ’πŸ– πŸ—πŸ‘Β° 𝒂= πŸπŸ“βˆ—π’”π’Šπ’ πŸ’πŸ– π’”π’Šπ’ πŸ—πŸ‘ 𝒂 𝒂=𝟏𝟏.𝟐

5 Example 1; Using the Law of Sines (AAS)
b) In βˆ†π΄π΅πΆ, π‘šβˆ π΄=48, π‘šβˆ π΅=93, and 𝐴𝐢=15, find 𝐴𝐡. A B C π’”π’Šπ’ 𝑩 𝒃 = π’”π’Šπ’ π‘ͺ 𝒄 πŸ’πŸ–Β° π’”π’Šπ’ πŸ—πŸ‘ πŸπŸ“ = π’”π’Šπ’ πŸ‘πŸ— 𝒄 𝒃 πŸπŸ“ π’„βˆ—π’”π’Šπ’ πŸ—πŸ‘ =πŸπŸ“βˆ—π’”π’Šπ’ πŸ‘πŸ— πŸ‘πŸ—Β° πŸ—πŸ‘Β° 𝒄= πŸπŸ“βˆ—π’”π’Šπ’ πŸ‘πŸ— π’”π’Šπ’ πŸ—πŸ‘ π‘ͺ=πŸπŸ–πŸŽβˆ’ πŸ—πŸ‘+πŸ’πŸ– π‘ͺ=πŸ‘πŸ—Β° 𝒄=πŸ—.πŸ“

6 Example 2; Using the Law of Sines (SSA)
b) In βˆ†πΎπΏπ‘€, 𝐿𝑀=9, 𝐾𝑀=14, and π‘šβˆ πΏ=105, find π‘šβˆ πΎ. π’”π’Šπ’ 𝑲 π’Œ = π’”π’Šπ’ 𝑳 𝒍 K L M π’”π’Šπ’ 𝑲 πŸ— = π’”π’Šπ’ πŸπŸŽπŸ“ πŸπŸ’ πŸπŸ’ πŸπŸ’βˆ—π’”π’Šπ’ 𝑲 =πŸ—βˆ—π’”π’Šπ’ πŸπŸŽπŸ“ π’”π’Šπ’ 𝑲 = πŸ—βˆ—π’”π’Šπ’ πŸπŸŽπŸ“ πŸπŸ’ πŸπŸŽπŸ“Β° πŸ— 𝑲= sin βˆ’πŸ πŸ—βˆ—π’”π’Šπ’ πŸπŸŽπŸ“ πŸπŸ’ 𝑲=πŸ‘πŸ–.πŸ’Β°

7 Example 2; Using the Law of Sines (SSA)
a) A ship has been at sea longer than expected and has only enough fuel to safely sail another 42 miles. Port City Lighthouse and Cove Town Lighthouse are located 40 miles apart along the coast. At sea, the captain cannot determine distances by observation. The triangle formed by lighthouses and the ship is shown. Can the ship sail safely to either lighthouse? P S C π’”π’Šπ’ 𝑺 𝒔 = π’”π’Šπ’ 𝑷 𝒑 πŸ•πŸŽΒ° π’”π’Šπ’ πŸ“πŸ– πŸ’πŸŽ = π’”π’Šπ’ πŸ•πŸŽ 𝒑 πŸ’πŸŽ π’Žπ’Š π’‘βˆ—π’”π’Šπ’ πŸ“πŸ– =πŸ’πŸŽβˆ—π’”π’Šπ’ πŸ•πŸŽ πŸ“πŸΒ° πŸ“πŸ–Β° 𝒑= πŸ’πŸŽβˆ—π’”π’Šπ’ πŸ•πŸŽ π’”π’Šπ’ πŸ“πŸ– 𝑺=πŸπŸ–πŸŽβˆ’ πŸ—πŸ‘+πŸ’πŸ– 𝒑=πŸ’πŸ’.πŸ‘ π’Žπ’Š. 𝑺=πŸ“πŸ–Β° Can’t go to Cove Town

8 Example 2; Using the Law of Sines (SSA)
a) A ship has been at sea longer than expected and has only enough fuel to safely sail another 42 miles. Port City Lighthouse and Cove Town Lighthouse are located 40 miles apart along the coast. At sea, the captain cannot determine distances by observation. The triangle formed by lighthouses and the ship is shown. Can the ship sail safely to either lighthouse? P S C π’”π’Šπ’ 𝑺 𝒔 = π’”π’Šπ’ π‘ͺ 𝒄 πŸ•πŸŽΒ° π’”π’Šπ’ πŸ“πŸ– πŸ’πŸŽ = π’”π’Šπ’ πŸ“πŸ 𝒄 πŸ’πŸŽ π’Žπ’Š π’„βˆ—π’”π’Šπ’ πŸ“πŸ– =πŸ’πŸŽβˆ—π’”π’Šπ’ πŸ“πŸ πŸ“πŸΒ° πŸ“πŸ–Β° 𝒄= πŸ’πŸŽβˆ—π’”π’Šπ’ πŸ“πŸ π’”π’Šπ’ πŸ“πŸ– 𝒄=πŸ‘πŸ•.𝟐 π’Žπ’Š. Can go to Port City

9 Example 2; Using the Law of Sines (SSA)
b) The right-fielder fields a softball between first base and second base as shown. If the right-fielder throws the ball to second base, how far does she throw the ball? RF 2nd 1st π’”π’Šπ’ 𝑹𝑭 πŸ”πŸŽ = π’”π’Šπ’ πŸπ’”π’• 𝒙 πŸ•πŸΒ° π’”π’Šπ’ πŸ•πŸ πŸ”πŸŽ = π’”π’Šπ’ πŸ’πŸŽ 𝒙 πŸ”πŸ–Β° πŸ”πŸŽ 𝒇𝒕 π’™βˆ—π’”π’Šπ’ πŸ•πŸ =πŸ”πŸŽβˆ—π’”π’Šπ’ πŸ’πŸŽ πŸ’πŸŽΒ° 𝒙= πŸ”πŸŽβˆ—π’”π’Šπ’ πŸ’πŸŽ π’”π’Šπ’ πŸ•πŸ 𝑹𝑭=πŸπŸ–πŸŽβˆ’ πŸ”πŸ–+πŸ’πŸŽ 𝒙=πŸ’πŸŽ.πŸ” 𝒇𝒕. 𝑹𝑭=πŸ•πŸΒ°

10 #42: Law of Sines Questions? Summarize Notes Homework Quiz

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