Solve a triangle for the AAS or ASA case

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EXAMPLE 1
Solve a triangle for the AAS or ASA case
SOLUTION
First find the angle A 180 107 25 48.
By the law of sines, you can write
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EXAMPLE 1
Solve a triangle for the AAS or ASA case
Solve for each variable.
Use a calculator.
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EXAMPLE 2
Solve the SSA case with one solution
SOLUTION
First make a sketch. Because A is obtuse and the
side opposite A is longer than the given adjacent
side, you know that only one triangle can be
formed. Use the law of sines to find B.
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EXAMPLE 2
Solve the SSA case with one solution
Law of sines
Multiply each side by 11.
Use inverse sine function.
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EXAMPLE 2
Solve the SSA case with one solution
Law of sines
Multiply each side by sin 35.1.
Use a calculator.
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EXAMPLE 3
Examine the SSA case with no solution
SOLUTION
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EXAMPLE 4
Solve the SSA case with two solutions
SOLUTION
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EXAMPLE 4
Solve the SSA case with two solutions
Use the law of sines to find the possible
measures of B.
Law of sines
Use a calculator.
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EXAMPLE 4
Solve the SSA case with two solutions
Now find the remaining angle C and side length c
for each triangle.
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EXAMPLE 5
Find the area of a triangle
Biology
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EXAMPLE 5
Find the area of a triangle
SOLUTION
The area of the region is
Write area formula.
Substitute.
Use a calculator.
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EXAMPLE 1
Solve a triangle for the SAS case
SOLUTION
Use the law of cosines to find side length b.
b2 a2 c2 2ac cos B
Law of cosines
b2 112 142 2(11)(14) cos 34
Substitute for a, c, and B.
Simplify.
Take positive square root.
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EXAMPLE 1
Solve a triangle for the SAS case
Use the law of sines to find the measure of angle
A.
Law of sines
Substitute for a, b, and B.
Multiply each side by 11 and Simplify.
Use inverse sine.
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EXAMPLE 2
Solve a triangle for the SSS case
SOLUTION
b2 a2 c2 2ac cos B
Law of cosines
272 122 202 2(12)(20) cos B
Substitute.
Solve for cos B.
Simplify.
Use inverse cosine.
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EXAMPLE 2
Solve a triangle for the SSS case
Now use the law of sines to find A.
Law of sines
Substitute for a, b, and B.
Multiply each side by 12 and simplify.
Use inverse sine.
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EXAMPLE 3
Use the law of cosines in real life
Science
The diagram at the right shows a set of
footprints for a dinosaur. Find the step angle B.
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EXAMPLE 3
Use the law of cosines in real life
SOLUTION
b2 a2 c2 2ac cos B
Law of cosines
3162 1552 1972 2(155)(197) cos B
Substitute.
Solve for cos B.
Simplify.
Use inverse cosine.
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EXAMPLE 4
Solve a multi-step problem
Urban Planning
SOLUTION
380
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EXAMPLE 4
Solve a multi-step problem
The area of the traffic triangle is about 18,300
square yards.