Heron's formula + The Law of Cosines - math problems

The Heron's formula is used to calculate the contents of a general triangle using the lengths of its sides. Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is:
$S= \sqrt {s(s-a)(s-b)(s-c)}$
, where
$s=\dfrac {a+b+c}{2}$
is the semiperimeter (half perimeter) of the triangle .

Number of problems found: 5

What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35 ´ and the edges a, b form an angle of 50.5°.
• Find the area
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
• Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
• Triangle
Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
• Heron backlaw
Calculate missing side in a triangle with sides 17 and 34 and area 275.

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