Depth angles

At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad


y =  272.265 m


v=30 m  A=90(32+50/60)=343657.1667  B=90(30+10/60)=359659.8333   t2=tan(B)=tan(59.8333)1.7205 t1=tan(A)=tan(57.1667)1.5497  tanA=xv+y tanB=x:y  x=y tanB  y tanB/tanA=v+y y(tanB/tanA1)=v  y=vt2/t11=301.7205/1.54971272.2651272.265 mv=30 \ \text{m} \ \\ \ \\ A=90 - (32 + 50/60)=\dfrac{ 343 }{ 6 } \doteq 57.1667 \ ^\circ \ \\ B=90 - (30 + 10/60)=\dfrac{ 359 }{ 6 } \doteq 59.8333 \ ^\circ \ \\ \ \\ t_{2}=\tan(B)=\tan(59.8333^\circ ) \doteq 1.7205 \ \\ t_{1}=\tan(A)=\tan(57.1667^\circ ) \doteq 1.5497 \ \\ \ \\ \tan A=\dfrac{ x }{ v+y } \ \\ \tan B=x:y \ \\ \ \\ x=y \cdot \ \tan B \ \\ \ \\ y \cdot \ \tan B / \tan A=v+y \ \\ y ( \tan B / \tan A - 1)=v \ \\ \ \\ y=\dfrac{ v }{ t_{2} / t_{1} - 1 }=\dfrac{ 30 }{ 1.7205 / 1.5497 - 1 } \doteq 272.2651 \doteq 272.265 \ \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!

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

Next similar math problems:

  1. 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?
  2. Angles of elevation
    height_building From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of t
  3. Triangle P2
    1right_triangle Can triangle have two right angles?
  4. 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.
  5. 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.
  6. 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?
  7. A drone
    drone A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at a height of 300 m above the plane of ABC. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in
  8. 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?
  9. 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.
  10. 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.
  11. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  12. KLM triangle
    trojuholnik_8 Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
  13. 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.
  14. How far
    lighthouse_1 From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
  15. 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?
  16. Obtuse angle
    10979326_654459541349455_1236723697_n The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
  17. 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?