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Area of a Triangle using Trigonometry

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This item is taken from IGCSE Mathematics (0580) Paper 43 of May/June 2014.

To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Trigonometry
   (b) Specific topic: Area of a Triangle
   (c) Formula Needed: 
IGCSE,mathematics,Cambridge,examination,past papers,revisions,triangles,trigonometry,angles,plane figures,sine,included angle
Let us take note that the area of the triangle is already given and the measure of one of the angles is missing. Using the formula above let us assign the parts of the triangle.
IGCSE,mathematics,Cambridge,examination,past papers,revisions,triangles,trigonometry,angles,plane figures,sine,included angle
Substitute the given measurements in the formula.
IGCSE,mathematics,Cambridge,examination,past papers,revisions,triangles,trigonometry,angles,plane figures,sine,included angle
Let us leave sin PQR on one side of the equation by dividing both sides by (1/2)(12)(17).
IGCSE,mathematics,Cambridge,examination,past papers,revisions,triangles,trigonometry,angles,plane figures,sine,included angle
Simplify, then find the measure of angle PQR.
IGCSE,mathematics,Cambridge,examination,past papers,revisions,triangles,trigonometry,angles,plane figures,sine,included angle
Therefore, the measure of angle PQR is 72.0 degrees.

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