The Law of Sines - practice problems
The Law of Sines is a trigonometric relationship that states in any triangle, the ratio of a side length to the sine of its opposite angle is constant for all three sides. Mathematically expressed as a/sin(A) = b/sin(B) = c/sin(C), where a, b, c are sides and A, B, C are their opposite angles. This law is particularly useful for solving triangles when given two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA, the ambiguous case). The ambiguous case can yield zero, one, or two possible triangles. Applications include navigation, surveying, astronomy, and physics problems involving force vectors. The Law of Sines complements the Law of Cosines for complete triangle solution methods.Directions: Provide a careful solution to each problem, showing all steps in your work.
Number of problems found: 51
- Laws
From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - The aspect ratio
The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle. - Sine theorem 2
From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°. - Big tower
From a tower 15 meters high and 30 meters away from the river, the width of the river appeared at an angle of 15°. How wide is the river in this place? - 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. - Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Parallelogram - area
Calculate the area of the parallelogram if a = 57cm, the diagonal u = 66cm, and the angle against the diagonal is beta β = 57°43' - 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? - Diamond diagonals
Calculate the diamond's diagonal lengths if its area is 156 cm² and the side length is 13 cm. - Triangle sides to angles
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. - 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 - ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Triangle angle area
Calculate the size of the largest angle in triangle ABC if a = 7 cm, b = 8 cm, and c = 13 cm. Calculate the area of the triangle, the height per side a. - 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. - Perimeter - ASA theorem
Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees. - Rhomboid
The rhomboid sides' dimensions are a= |AB|=5cm, b = |BC|=6 cm, and the angle's size at vertex A is 60°. What is the length of the diagonal AC? - Hypotenuse and center
Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the area of triangle ABC if the line on the hypotenuse is 0.2 dm long and if angle ∢ACS is 30°. - Cosine
Cosine and sine theorem: Calculate all unknown values (side lengths or angles) from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm - Cosine
Cosine and sine theorem: Calculate all unknown values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? ° - Triangle solving calculation
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.
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