Right triangle + The Law of Cosines - practice problems
Number of problems found: 30
- Laws
From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - The angle of view
Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other. - Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and a 10 cm long arm. What is the length of the medians? - Triangle ABC
Triangle ABC has side lengths m-1, m-2, and m-3. What has to be m to be a triangle a) rectangular b) acute-angled?
- Triangle and its heights
Calculate the length of the sides of the triangle ABC if va=5 cm, vb=7 cm and side b are 5 cm shorter than side a. - ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - The pond
We can see the pond at an angle of 65°37'. Its endpoints are 155 m and 177 m away from the observer. What is the width of the pond? - Calculate triangle
In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and area if given a=40cm, b=57cm, and c=59cm. - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t
- 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. - Two groves
Two groves A B are separated by a forest. Both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B if AC = 5004 m, BC = 2600 m, and angle ABC = 53° 45'? - Graphically 7004
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 - Determine 8202
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. - 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?
- Isosceles 7929
ABCD isosceles trapezoid. A = 6cm, e = 7cm and delta angle = 105 °. Calculate the remaining pages. - Determine 8133
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 - A rhombus
A rhombus has sides of the length of 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus. - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Triangle SAS
Calculate the triangle area and perimeter if the two sides are 105 dm and 68 dm long and angle them clamped is 50 °.
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