The Law of Sines - practice problems
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 51
- Laws
From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - 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. - 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 - Calculate 81757
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. - 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°. - Circumscribed circle
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle.
- Sine theorem 2
From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°. - Two artillery
Objective C we observe from two artillery observatories, A and B, which are 975 m apart. The size of the BAC angle is 63°, and the size of ABC is 48°. Calculate the distance of points A and C. - 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 =? ° - The aspect ratio
The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle. - ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - River
From the observatory 18 m high and 31 m from the riverbank, river width appears in the visual angle φ = 20°. Calculate the width of the river. - Determine 81756
The area for shooting training has the shape of a trapezoid, the parallel sides of which are 36m, 21m long, and the remaining sides are 14m, 16m long. Determine the size of the interior angles with a longer base.
- 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. - Magnitudes 64704
The triangle ABC determines the size of the sides a and b and the magnitudes of the interior angles β and γ, given c = 1.86 m, the line on the side c is 2.12 m, and the angle alpha is 40 ° 12 '. - 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.
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