Clock hands

Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours.

Correct result:

A =  75 °
B =  60 °
C =  45 °

Solution:

φ=360/12=30∘ α=(6−2)⋅ φ=(6−2)⋅ 30=120∘ β=(11−6)⋅ φ=(11−6)⋅ 30=150∘ γ=(2+12−11)⋅ φ=(2+12−11)⋅ 30=90∘  A=β/2=150/2=75∘
B=α/2=120/2=60∘
C=γ/2=90/2=45∘

Try another example


We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Do you want to convert time units like minutes to seconds?
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Clock hands
    watch_3 The hands on the clock shows the time 12 hours and 2 minutes. Calculate the size of a sharp angle between clock hands three hours later.
  • Interior angles
    circle_inscribed_polygon In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
  • Circumferential angle
    uhly Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC.
  • Clock Tower
    clock_3 What angle is betwenn hands on Clock Tower when show 17 hours and 35 minutes?
  • Hands
    soviet_watch The clock shows 12 hours. After how many minutes will angle between the hour and minute hand 90°? Consider the continuous movement of both hands hours.
  • Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  • Triangle angles
    triangles_2 The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
  • Internal and external angles
    inner_outer_angles_triangle Calculate the remaining internal and external angles of a triangle, if you know the internal angle γ (gamma) = 34 degrees and one external angle is 78 degrees and 40 '. Determine what kind of triangle it is from the size of its angles.
  • Little hand
    clock2_1 What angle shifted little hand on the clock after one hour and 38 minutes?
  • Inscribed triangle
    obluk To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
  • Smallest internal angle
    angles_3 Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
  • Internal angles
    triangle_5 Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.
  • Angles
    triangle The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
  • The chord
    Tetiva The side of the triangle inscribed in a circle is a chord passing through the circle center. What size are the internal angles of a triangle if one of them is 40°?
  • Angles in triangle
    trigonometry The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
  • Diagonals
    stvorec_7 Draw a square ABCD whose diagonals have a length of 6 cm
  • Prism
    prism-square The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?