# The Law of Sines - practice problems

Direction: Solve each problem carefully and show your solution in each item.#### Number of problems found: 42

- Laws

From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - Determine 18223

From the sine theorem, determine the ratio of the sides of a triangle whose angles are 30 °, 60 °, and 90 °. - Triangle 2668

The triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the sizes of the angles and the area of this triangle. - The aspect ratio

The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle. - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Two triangles SSA

We can form two triangles with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14 - Rhomboid

The rhomboid sides' dimensions are a= 5cm, b = 6 cm, and the angle's size at vertex A is 60°. What is the length of the side AC? - Big tower

From the tower, which is 15 m high, and 30 m from the river, the river's width appeared at an angle of 15°. How wide is the river in this place? - Cosine

Cosine and sine theorem: Calculate all missing values from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm - ABCD

AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Triangle 75

Triangle ABC has angle C bisected and intersected AB at D. Angle A measures 20 degrees, and angle B measures 40 degrees. The question is to determine AB-AC if length AD=1. - The mast

We see the top of the pole at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole? - Parallelogram 6049

Calculate the area of the parallelogram if a = 57cm, the diagonal u = 66cm, and the angle against the diagonal is beta β = 57° 43' - Calculate 4422

Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees. - Diamond diagonals

Calculate the diamond's diagonal lengths if its area is 156 cm² and the side length is 13 cm. - Children playground

The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles. - Observer

The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence? - Viewing angle

The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - Triangle's 9731

Solve the triangle ABC if the side a = 52 cm, the height on the other side is vb = 21 cm, and the triangle's area is S = 330 cm². - River

From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river.

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