# The Law of Sines + The Law of Cosines - math problems

1. Laws From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
2. Inner angles The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
3. ABCD AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
4. Largest angle of the triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
5. Children playground The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.

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Cosine rule uses trigonometric SAS triangle calculator.