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Use trigonometry if another angle is given. Use Pythagoras' theorem if the hypotenuse is given. Multiply the area by 2 and divide it by its height if the area is given. Or simply measure it.
There is nothing in the question to justify an assumption that the angle is a vertex of a triangle. Even if it were, there is no justification for assuming that it is a right angled triangle. So the use of ratios of sides of a triangle are totally inappropriate.In the circumstances, the only realistic way is to use a calculator. Make sure that the calculator's mode is set to the correct measurement unit for the angle - degrees or radians - and use the cosine or sine function.Spreadsheets such as Excel only use angles measured in radians. So, if given the angle in degrees, multiply the value by pi/180 and then use the appropriate trigonometric function.
The answer depends on the sequence. Different sequences may be used in different circumstances.
Measure it or use trigonometry if the 'included' angle is given.
use your ruler to measure the sides