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5-Minute Check Lesson 5-7A. Math ador Gameplan. Section 5.7: The Ambiguous Case for Law of Sines CA Standards: Algebra 2 Review Daily Objective (): Students will be able to (1) determine whether a triangle has zero, one, or two solutions, and (2) solve triangles using Law of Sines .

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MathadorGameplan

Section 5.7:The Ambiguous Case for Law of Sines

CA Standards: Algebra 2 Review

Daily Objective ():

Students will be able to (1) determine whether a triangle has zero, one, or two solutions, and (2) solve triangles using Law of Sines.

Homework #: page 324 (#11 to 33 all)

the law of sines
The Law of SINES

For any triangle (right, acute or obtuse), you may use the following formula to solve for missing sides or angles:

use law of sines when
Use Law of SINES when ...
  • AAS - 2 angles and 1 adjacent side
  • ASA - 2 angles and their included side
  • SSA(this is an ambiguous case)

you have 3 dimensions of a triangle and you need to find the other 3 dimensions - they cannot be just ANY 3 dimensions though, or you won’t have enough info to solve the Law of Sines equation. Use the Law of Sines if you are given:

the ambiguous case ssa
The Ambiguous Case (SSA)

When given SSA (two sides and an angle that is NOT the included angle) , the situation is ambiguous. The dimensions may not form a triangle, or there may be 1 or 2 triangles with the given dimensions.

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Find all solutions for each triangle.

If no solutions exist, write none.

a. A = 25°, a = 15, b = 20

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While riding on a roller coaster at an amusement park, passengers climb at a 45° angle along 418 feet of track in order to reach the highest point of the ride.

Once at the top, they plunge down 300 feet of track.

What is the angle of depression of the roller coaster?

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