Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.

Correct result:

X =  72.452 °

Solution:

a=4 cm v=6 cm  s=v2+(a/2)2=62+(4/2)2≐2 10 cm≐6.3246 cm  tan⁡X=s/(a/2)  X1=arctan⁡(2⋅ s/a)=arctan⁡(2⋅ 6.3246/4)≐1.2645 rad  X=X1→ ∘=X1⋅ 180π  ∘=1.26451895763⋅ 180π  ∘=72.452  ∘=72.452∘=72∘27′6"a=4 \ \text{cm} \ \\ v=6 \ \text{cm} \ \\ \ \\ s=\sqrt{ v^2 + (a/2)^2 }=\sqrt{ 6^2 + (4/2)^2 } \doteq 2 \ \sqrt{ 10 } \ \text{cm} \doteq 6.3246 \ \text{cm} \ \\ \ \\ \tan X=s / (a/2) \ \\ \ \\ X_{1}=\arctan( 2 \cdot \ s/a)=\arctan( 2 \cdot \ 6.3246/4) \doteq 1.2645 \ \text{rad} \ \\ \ \\ X=X_{1} \rightarrow \ ^\circ =X_{1} \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =1.26451895763 \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ =72.452 \ \ ^\circ =72.452 ^\circ =72^\circ 27'6"

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
See also our 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

Next similar math problems:

  • The angle of lines
    lines Calculate the angle of two lines y=x-21 and y=-2x+14
  • 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.
  • Pyramid
    jehlan Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
  • Maple
    tree_javor Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
  • 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?
  • Black diamond run
    ski Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet.
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • Road drop
    atan On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
  • 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?
  • 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.
  • Hole's angles
    Trapezium2-300x199 I am trying to find an angle. The top of the hole is .625” and the bottom of the hole is .532”. The hole depth is .250” what is the angle of the hole (and what is the formula)?
  • If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  • Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  • Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  • Slope of the pool
    swimming_pool Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 1.13 m (for children) and depth at end is 1.84 m (for swimmers). Slope express as percentage and as angle in degrees.
  • Bevel
    zkoseni I have bevel in the ratio 1:6. What is the angle and how do I calculate it?
  • Line
    skew_lines It is true that the lines that do not intersect are parallel?