Law of cosines - practice problems - page 4 of 5
Instructions: For each problem, solve carefully and show your complete working.Number of problems found: 85
- Inner angles
The inner angles of the triangle are 30°, 45°, and 105° and its longest side is 10 cm. Calculate the shortest side length, and write the result in cm up to two decimal places. - Course to airport
The plane flew from airport m on a course of 132° to airport n, then from n to p on a course of 235°. The distance between the airport's mn is 380 km, np 284 km. What will be the return course to m, and what is the distance between the airport's pm? - Two boats
Two boats are located from a height of 150m above the lake's surface at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the lake's surface. - Circular railway
The railway connects points A, B, and C in a circular arc, whose distances are | AB | = 30 km, AC = 95 km, and BC | = 70 km. How long will the track be from A to C? - In trapezoid 3
In trapezoid ABCD, the following elements are given: lengths of the parallel sides a = 20 cm and c = 11 cm, angle α = 63°36', and angle β = 79°36'. Calculate the lengths of the other two sides and the sizes of the remaining angles. - Parallelogram - area
Calculate the area of the parallelogram if the sides are a = 80, b = 60 long, and the size of the diagonal angle is 60°. - Triangle SAS
Calculate the triangle area and perimeter if the two sides are 46 m and 33 m long and angle them clamped is 170 °. - Distance Between Boats An observer watches two boats at depth angles of 64° and 48° from the top of the hill, which is 75 m above the lake level. Determine the distance between the boats if both boats and the observer are in the same vertical plane.
- Binibini
Binibini owns a triangular residential lot bounded by two roads intersecting at 70°. The sides of the lot along the road are 62 m and 43 m, respectively. Find the length of the fence needed to enclose the lot. (express answers to the nearest hundredths) - Triangulation - 3 places
Determine the distance between two inaccessible places K, L, if the angles KAL=62°10", LAB=41°23", KBL=66°34", and LBA were measured from points A, B, which are 870 m apart = 34°52". Thank you. - Inaccessible direct
Determine the distance between two inaccessible places P, Q, if the distance between two observation points A, B is 2000 m and if you know the size of the angles QAB = 52°40''; PBA = 42°01''; PAB = 86°40'' and QBA = 81°15''. The considered locations A, B, - Observatories A,B
The target C is observed from two artillery observatories, A and B, 296 m apart. At the same time, angle BAC = 52°42" and angle ABC = 44°56". Calculate the distance of the target C from observatory A. - Boat in the lake
A boatman walks along the ship's deck at a constant speed of 5 km/h in a direction that forms an angle of 60° with the direction of the ship's speed. The boat moves with respect to the lake's calm surface at a constant speed of 10 km/h. Determine graphica - Triangle
Plane coordinates of vertices: K[9, 5] L[-4, 8] M[3, 20] give Triangle KLM. Calculate its area and its interior angles. - Tunnel - quadrilateral
How long will tunnel AB be, given distances AD = 35 m, DC = 120 m, CB = 85 m, angle ADC = 105°, and angle BCD = 71°, where ABCD is a quadrilateral? - An azimuth
The patrol had started at a designated marching angle (an azimuth) of 13°. After 9 km, the azimuth's angle changed to 62°. The patrol went 10 km in this direction. Find the distance from where the patrol started. - Distance with Obstacle Measurement
Determine the distance between two places, M, and N, between which there is an obstacle so that place N is not visible from place M. The angles MAN = 130°, NBM = 109°, and the distances |AM| = 54, |BM| = 60, while the points A, B, and M lie on one straigh - Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each of the two forces. - Mass point
Two equal forces of 30 Newtons act on a mass point. Find the magnitude of the resultant force if these forces form an angle of 42°. - Three vertices
The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A.
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