contestada

In a certain right triangle, one angle measures pi/11, and the side adjacent to that angle has a length of 13. Find the exact measure of the other non-right triangle and the lengths of the other two sides.

Respuesta :

sqdancefan

9514 1404 393

Answer:

  • angle: 9π/22
  • opposite side: 13tan(π/11) ≈ 3.817
  • hypotenuse: 13sec(π/11) ≈ 13.549

Step-by-step explanation:

The other acute angle in the triangle is the complement of the given one.

  π/2 -π/11 = (11 -2)π/11 = 9π/11 . . . . other acute angle

The trig relation applicable to finding the length of the opposite side is ...

  Tan = Opposite/Adjacent

  tan(π/11) = Opposite/13

  Opposite = 13·tan(π/11) ≈ 3.817

The trig relation relevant to finding the length of the hypotenuse is ...

  Cos = Adjacent/Hypotenuse

  cos(π/11) = 13/Hypotenuse

  Hypotenuse = 13/cos(π/11) = 13sec(π/11) ≈ 13.549

Otras preguntas