Sunday, March 16, 2014

BQ#1: Unit P Concept 1-2: Law of Sines SSA and Area of an oblique triangle

2. SSA is ambiguous because referencing to our unit circle sine can be positive in two quadrants that are less than 180(a triangle's angles add up to 180), which is the first and second quadrant(of the reference angle). Also, it is ambiguous because for AAS and ASA we had the angles or we only had to find one by using the triangle sum theorem.

4.The area of an oblique formula is derived from the geometry are of a triangle formula, which is 1/b*h. If we draw a triangle an we do not know it's  height in order to find the area, then we can make that triangle into two triangles by drawing a line from the top (m<B) to the middle(between m<A and m<C or just in the middle of side b). We can label that h because that will be the height of the triangle.Next, we can take the sin of m<A and it will be h/c (SOH=OPPOSITE/HYPOTENUSE). Then, we can multiply c to both sides for it can cancel in the denominator and we are left with csin m<A=h and now we can plug in h in A=1/2bh and we get A=1/2b(asinC). However, this can be written in many ways depending on what you are given. For example, A=1/2bcsinA;A=1/2acsinB;A=1/2absinC.
www.ck12.org/book/CK-12-Trigonometry-Concepts/r2/section/5.4/

References:http://www.ck12.org/book/CK-12-Trigonometry-Concepts/r2/section/5.4/

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