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Law of Sines Help?

asked Nov 10, 2015 in GEOMETRY by dneesy Rookie

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commented Nov 10, 2015 by Lucy Mentor

http://s292.photobucket.com/user/dneesy1994/media/Scan_20151109_zpsbgs6ztno.png.html?sort=3&o=0#

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http://s292.photobucket.com/user/dneesy1994/media/Scan_20151109%202_zpsdd0sdywe.png.html

There are two pictures

commented Nov 10, 2015 by dneesy Rookie

10 Answers

(1)

Step 1:

Side of the triangle is .

Angles of the triangle are .

Sum of the angles in a triangle is .

The third angle is .

Step 2:

Find the length of side .

Apply Sine law: .

Consider .

Substitute and .

Solution:

answered Nov 10, 2015 by Lucy Mentor
edited Nov 10, 2015 by Lucy

(5)

Step 1:

Consider the triangle .

Redraw the diagram labeling the vertices.

The sides of a triangle are and .

The angle of triangle is .

Solve the triangle by using the Law of Sines.

The Law of Sines: .

Consider .

Substitute , and in .

.

Step 2:

The sum of three angles in a triangle is .

Substitute and .

.

Find the length of the .

Using Law of Sines .

Substitute , and in .

.

Solution:

, and .

answered Nov 10, 2015 by Sammi Mentor
edited Nov 10, 2015 by Sammi

(2)

Side of the triangle is .

Angle of the triangle is .

Law of sines:

Either angle or side is needed to apply law of sines.

For an example, consider

To find the value of angle , side has to be known.

answered Nov 10, 2015 by Lucy Mentor
edited Nov 10, 2015 by Lucy

(6)

Solving an oblique triangle using the Law of Sines:

a. The measure of an angle must be known.

b. The length of the side opposite the known angle must be known.

c. At least one more side or one more angle must be known.

Therefore, the Law of Sines can be used to solve the SAA, ASA, and SSA cases.

1. Two angles and a side opposite one of the angles is known (AAS).

2. Two angles and the side between the angles is known (ASA).

3. Two sides and an angle opposite one of them (SSA).

answered Nov 10, 2015 by Sammi Mentor

(7)

The sides of a triangle are and .

The angle of triangle .

Since two sides and an angle opposite to one of them are known, the case is SSA triangle.

The law of sines can be applied for SSA triangle.

Therefore, Law of sines can be applied.

answered Nov 10, 2015 by Sammi Mentor
edited Nov 10, 2015 by Sammi

(10)

Observe the figure:

The three sides of the triangle are known forming the case of SSS triangle.

Law of sines for the triangle: .

The Law of sines cannot be applied to SSS triangle.

Therefore, Law of sines cannot be applied.

answered Nov 10, 2015 by Lucy Mentor
edited Nov 10, 2015 by Lucy

(4)

From the result of (3), Angle .

Other angle in triangle is .

Sum of the three angles in a triangle is .

Law of Sines: .

Consider .

Substitute , and in .

answered Nov 10, 2015 by cameron Mentor
edited Nov 11, 2015 by cameron

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