Area of a Triangle using Trigonometry

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: 

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.

Substitute the given measurements in the formula.

Let us leave sin PQR on one side of the equation by dividing both sides by (1/2)(12)(17).

Simplify, then find the measure of angle PQR.

Therefore, the measure of angle PQR is 72.0 degrees.

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