BQ #1: Unit P Concept 1 & 4 - Law of Sines and Area Formula

1. Law of Sines 

The Law of Sines has great use when only given a few measurements of a not right triangle when needing all measurements. Figuring out the measurements of the angles and sides of a non right triangle is a bit more complex than with special right triangles because we cannot use SOH CAH TOA. Instead we use the law of sin to figure out one angle/side at a time. For example, in the picture below if we are only given Angle C, side b and Angle A, we can derive the law of sines to figure out the rest of the measurements. Given the measurements of two angles, we add them and divide by 180 to find the third angle. Once we find the third angle we match up sin (angle) B/ sin (side) b = sin (angle) of either A or C and continue that until all sides are found. 

(https://www.google.com/search?hl=en&site=imghp&tbm=isch&source=hp&biw=1680&bih=949&q=non+right+triangles&oq=non+right+triangles&gs_l=img.3..0.1425.6210.0.6666.23.21.2.0.0.0.150.1641.19j2.21.0....0...1ac.1.37.img..2.21.1450.ngevANF7olE#facrc=_&imgdii=_&imgrc=OMDCBtQcvuCROM%253A%3BibnpwnU4btR6lM%3Bhttp%253A%252F%252Fwww.drcruzan.com%252FImages%252FTrigNonRight%252FNonRightTriangleLabeling.png%3Bhttp%253A%252F%252Fwww.drcruzan.com%252FMathNonRightTrig.html%3B317%3B196) 

 4. Area formulas

Finding the area of oblique triangles all comes from the formula derived from the area of a triangle
A = 1/2bh. Using the picture below, we know that sinC= h/a, so to derive it to equal to the h we therefore get h = asinC. Next we substitute in our regular area equation for h and we get A= 1/2b(asinC). When solving for these triangles we are most likely going to be given two sides and one angle. The two sides are imputed into the equation as a and b. The angle that is given is always found with the use of sin. 

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