The mast

The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?

Correct result:

h =  23.66 m

Solution:

tan⁡(60∘)=h/x tan⁡(45∘)=h/(x+10)  x=h/tan⁡(60∘)=h⋅ t1 t1=1/tan⁡60∘=tan⁡π/3=0.57735 t2=tan⁡45∘=tan⁡π/4=1  t2⋅ (h⋅ t1+10)=h t2⋅ h⋅ t1+10⋅ t2=h  h=10⋅ t21−t2⋅ t1=10⋅ 11−1⋅ 0.5774=23.66 m\tan(60^\circ )=h/x \ \\ \tan(45^\circ )=h/(x+10) \ \\ \ \\ x=h / \tan(60^\circ )=h \cdot \ t_{1} \ \\ t_{1}=1/ \tan 60 ^\circ =\tan π/3=0.57735 \ \\ t_{2}=\tan 45 ^\circ =\tan π/4=1 \ \\ \ \\ t_{2} \cdot \ (h \cdot \ t_{1}+10)=h \ \\ t_{2} \cdot \ h \cdot \ t_{1}+10 \cdot \ t_{2}=h \ \\ \ \\ h=\dfrac{ 10 \cdot \ t_{2} }{ 1-t_{2} \cdot \ t_{1} }=\dfrac{ 10 \cdot \ 1 }{ 1-1 \cdot \ 0.5774 }=23.66 \ \text{m}

Try another example


We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Do you want to convert length units?
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:

  • 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?
  • 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?
  • 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?
  • 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.
  • 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.
  • 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.
  • 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.
  • If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  • Cable car
    lanovka Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
  • 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.
  • Depth angle
    cliff From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
  • Perimeter of triangle
    rt_triangle_1 In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
  • Trapezium ABCD
    lichobeznik_5 In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
  • 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.
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?