Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.

Correct answer:

a =  39.3867 dm
b =  23.2337 dm
c =  26.7934 dm

Step-by-step explanation:

$$\begin{gathered} u=53\text{ dm } \\ A=42\text{ ° } \\ B=64\text{ ° } \\ a=u\cdot \cos A\mathrm{°}=u\cdot \cos 42\mathrm{°}=53\cdot \cos 42\mathrm{°}=53\cdot 0.743145=39.387=39.3867\text{ dm} \end{gathered}$$

$b=u\cdot \cos B\mathrm{°}=u\cdot \cos 64\mathrm{°}=53\cdot \cos 64\mathrm{°}=53\cdot 0.438371=23.234=23.2337\text{ dm}$

$$\begin{gathered} u_2=\sqrt{a^2+b^2}=\sqrt{39.3867^2+23.2337^2}\doteq 45.7287\text{ dm } \\ c=\sqrt{u^2-u_2^2}=\sqrt{53^2-45.7287^2}=26.7934\text{ dm} \end{gathered}$$

Try another example

Related math problems and questions:

• Cuboid
  Find the dimensions of cuboid a, b, c; if diagonal d=9 dm has an angle with edge α=55° and has an angle with edge b β=58°
• Diagonals of a prism
  The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base.
• Angle of diagonal
  The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
• Resultant force
  Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
• Elevation angles
  From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
• Base diagonal
  In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid.
• Space diagonal angles
  Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
• Prism diagonal
  The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
• Clouds
  From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
• Tetrahedral pyramid
  Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'.
• Bearing
  A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• Quadrilateral oblique prism
  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°.
• Right triangle trigonometrics
  Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
• Angle of diagonals
  Calculate the perimeter and the area of a rectangle if its diagonal is 14 cm and the diagonals form an angle of 130°.
• Deviation of the lines
  Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
• Four sided prism
  Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane.