Three pillars

On a straight road, three pillars are 6 m high at the same distance of 10 m. At what angle of view does Vlado see each pillar if it is 30 m from the first and his eyes are at 1.8 m high?

Correct answer:

A =  11.4032 °
B =  8.5707 °
C =  6.8633 °

Step-by-step explanation:

n=3 h=6 m a=10 m l1=30 m o=1.8 m   tanα=o:l1 α=180πarctan(o/l1)=180πarctan(1.8/30)3.4336  tanβ=(ho):l1 β=180πarctan((ho)/l1)=180πarctan((61.8)/30)7.9696  A=α+β=3.4336+7.9696=11.4032=112412"
θ=arctan(o/(l1+a))+arctan((ho)/(l1+a))=arctan(1.8/(30+10))+arctan((61.8)/(30+10))0.1496 rad B=θ=θ 180π=0.1496 180π=8.571=8.5707=83414"
Ψ=arctan(o/(l1+2 a))+arctan((ho)/(l1+2 a))=arctan(1.8/(30+2 10))+arctan((61.8)/(30+2 10))0.1198 rad C=Ψ=Ψ 180π=0.1198 180π=6.863=6.8633=65148"



We will be pleased if You send us any improvements to this math problem. Thank you!



avatar




Tips to related online calculators
See also our right triangle calculator.
See also our trigonometric triangle calculator.

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

Related math problems and questions:

  • 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?
  • Powerplant chimney
    komin2 From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
  • Steeple
    church_tower We see the church tower from the road at an angle of 52°. When we zoom out to 29 meters away, it can be seen at an angle of 21°. How high is it?
  • 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?
  • Power line pole
    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.
  • Road
    12perctent The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
  • Traffic sign
    cyklo2 There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
  • Traffic laws
    car_lights Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
  • Right triangle trigonometrics
    triangle2 Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
  • Road
    route-66 The average climb of the road is given by ratio 1:15. By what angle road average climb?
  • A boy
    angles_6 A boy of height 1.7m is standing 30m away from the flagstaff on the same level ground. He observes that the angle of deviation of the top of flagstaff is 30 degrees. Calculate the height of flagstaff.
  • Aircraft
    aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
  • Balloon and bridge
    hlbkovy_angle From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
  • 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.
  • 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?
  • Statue
    michelangelo On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
  • Slope of the pool
    swimming_pool Calculate slope (rise:run) of the bottom of the swimming pool long 30 m. Water depth at beginning of the pool is 1.13 m (for children) and depth at the end is 1.84 m (for swimmers). Slope express as percentage and as the angle in degrees.