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°.

Correct answer:

o =  37.2099 cm
S =  75.0724 cm²

Step-by-step explanation:

$$\begin{gathered} u=14\text{ cm } \\ \alpha =130\text{ ° } \\ \beta =\alpha \mathrm{/}2=130\mathrm{/}2=65\text{ ° } \\ \sin \beta =a:u=12.6883:14=0 \\ a=u\cdot \sin \beta \mathrm{°}=u\cdot \sin 65\mathrm{°}=14\cdot \sin 65\mathrm{°}=14\cdot 0.906308=12.68831\text{ cm } \\ \cos \beta =b:u=5.9167:14=0 \\ b=u\cdot \cos \beta \mathrm{°}=u\cdot \cos 65\mathrm{°}=14\cdot \cos 65\mathrm{°}=14\cdot 0.422618=5.91666\text{ cm } \\ o=2\cdot (a+b)=2\cdot (12.6883+5.9167)=37.2099\text{ cm} \end{gathered}$$

$S=a\cdot b=12.6883\cdot 5.9167=75.0724{\text{cm}}^2$

Try another example

Related math problems and questions:

• 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 °.
• 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)
• 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.
• Diagonal
  Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.
• Diagonal
  The diagonal of the rectangle has a length of 41.4 cm. The angle between the diagonal and longer side of the rectangle is 26°. Calculate the area of the rectangle.
• Rhombus
  One angle of a rhombus is 136°, and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
• Calculate
  Calculate the area of triangle ABC, if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
• Perimeter of triangle
  In the triangle, ABC angle A is 60° angle B is 90°, and side size c is 15 cm. Calculate the triangle circumference.
• Diagonals of the rhombus
  How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm²?
• Parallelogram diagonals
  Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm and the angle formed by them is 30 degrees.
• 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'.
• Right triangle
  Calculate the missing side b and interior angles, perimeter, and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
• Triangle ABC v2
  Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
• Triangle SAA
  The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
• Building
  The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
• Diamond and angles
  Find the area of a diamond with a side of 5 cm if you know that the internal angles in the diamond are 60° and 120°.
• Right angle
  In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.