The Law of Cosines + right triangle - 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? - 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. - 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. - 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? - ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Isosceles 7929
ABCD isosceles trapezoid. A = 6cm, e = 7cm and delta angle = 105 °. Calculate the remaining pages. - 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? - 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. - Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords. - 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. - Measurements of a triangle
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft - 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 - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Cosine
Cosine and sine theorem: Calculate all missing values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? ° - 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'? - Parallelogram 5027
Calculate the area of the parallelogram if the side sizes are a = 80, b = 60, and the size of the diagonal angle is 60°.
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