EQL triangle

Calculate inradius and circumradius of equilateral triangle with side a=77 cm.

Correct result:

r1 =  22.2 cm
r2 =  44.5 cm

Solution:

 tan⁡30∘=r1772 r1=772tan⁡30∘=22.2 cm \ \\ \tan 30 ^\circ = \dfrac{ r_1 }{ \dfrac{ 77}{2 } } \ \\ r_1= \dfrac{ 77}{2 } \tan 30 ^\circ = 22.2 \ \text{cm}
 cos⁡30∘=772r2 r2=772/cos⁡30∘=44.5 cm \ \\ \cos 30 ^\circ = \dfrac{ \dfrac{ 77}{2 } }{ r_2 } \ \\ r_2= \dfrac{ 77}{2 } / \cos 30 ^\circ = 44.5 \ \text{cm}

Try calculation via our triangle calculator.


Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
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   video2

Next similar math problems:

  • OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
  • Perimeter of circle
    thalet_1 Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
  • Four ropes
    vysilac TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment
  • Broken tree
    stromy_4 The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree.
  • Stairway
    schody Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
  • Two parallel chords
    chords_equall The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle.
  • Circumscribing
    thales Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
  • Reflector
    lamp Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
  • Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Windbreak
    vichrica A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
  • Ladder
    rebrik_2 The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder.
  • Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
  • Horizon
    lighthouse The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
  • Tree
    strom How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
  • Flowerbed
    triangle_flowers.JPG Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
  • High wall
    mur I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?