# The Law of Cosines + sine - math problems

#### Number of problems found: 14

• Angles by cosine law
Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
• ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
• Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
• Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What is the length of medians?
• 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 two forces.
• 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.
• Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than 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.
• Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
• 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 point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
• Two boats
Two boats are located from a height of 150m above the surface of the lake 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 surface of the lake.
• Triangle SAS
Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
• Inner angles
The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.