Power line pole

From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.

Result

h =  11.567 m

Solution:

c=30 m A=18  B=10  t0=tanA=tan18 =0.32492 t1=tanB=tan10 =0.176327=0.17633 h/x=tanA=t0 h/(x+c)=tanB=t1  x=h/t0 h/(h/t0+c)=t1 h=t1 (h/t0+c) h=t1/t0 h+c t1 h(1t1/t0)=c t1  h=c t11t1/t0=30 0.176310.1763/0.324911.566911.567 mc=30 \ \text{m} \ \\ A=18 \ ^\circ \ \\ B=10 \ ^\circ \ \\ t_{0}=\tan A ^\circ =\tan 18^\circ \ =0.32492 \ \\ t_{1}=\tan B ^\circ =\tan 10^\circ \ =0.176327=0.17633 \ \\ h/x=\tan A=t_{0} \ \\ h/(x+c)=\tan B=t_{1} \ \\ \ \\ x=h/t_{0} \ \\ h/(h/t_{0}+c)=t_{1} \ \\ h=t_{1} \cdot \ (h/t_{0}+c) \ \\ h=t_{1}/t_{0} \cdot \ h+c \cdot \ t_{1} \ \\ h(1 -t_{1}/t_{0})=c \cdot \ t_{1} \ \\ \ \\ h=\dfrac{ c \cdot \ t_{1} }{ 1 -t_{1}/t_{0} }=\dfrac{ 30 \cdot \ 0.1763 }{ 1 -0.1763/0.3249 } \doteq 11.5669 \doteq 11.567 \ \text{m}



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.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

 

 

Next similar math problems:

  1. Tree
    stromcek_1 Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
  2. The Eiffel Tower
    Eiffel-Tower-Paris The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
  3. Steeple
    church_tower Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
  4. The rescue helicopter
    helicopter The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?
  5. Isosceles triangle 10
    iso_23 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
  6. 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.
  7. 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?
  8. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  9. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  10. Building
    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?
  11. 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?
  12. Reference angle
    anglemeter Find the reference angle of each angle:
  13. Ladder slope
    rebrik33 What is the slope of a ladder 6.2 m long and 5.12 m in height.
  14. Cosine
    theta Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
  15. 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?
  16. One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  17. Trigonometry
    sinus Is true equality? ?