The angle of view

Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.

Result

A =  34.919 °

Solution:

a=16 m b=18 m c=27 m  a2=b2+c22 b c cosA  x=a2+b2+c22 b c=162+182+2722 18 277979720.82  A=180πarccos(x)=180πarccos(0.82)34.919334.919345510"a=16 \ \text{m} \ \\ b=18 \ \text{m} \ \\ c=27 \ \text{m} \ \\ \ \\ a^2=b^2+c^2 - 2 \cdot \ b \cdot \ c \cdot \ \cos A \ \\ \ \\ x=\dfrac{ -a^2+b^2+c^2 }{ 2 \cdot \ b \cdot \ c }=\dfrac{ -16^2+18^2+27^2 }{ 2 \cdot \ 18 \cdot \ 27 } \doteq \dfrac{ 797 }{ 972 } \doteq 0.82 \ \\ \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arccos(x)=\dfrac{ 180^\circ }{ \pi } \cdot \arccos(0.82) \doteq 34.9193 \doteq 34.919 ^\circ \doteq 34^\circ 55'10"

Try calculation via our triangle calculator.




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.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  1. 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.
  2. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  3. The spacecraft
    Sputnik_670 The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered
  4. Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  5. 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?
  6. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  7. Scalene triangle
    triangles_1 Solve the triangle: A = 50°, b = 13, c = 6
  8. Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  9. 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.
  10. Four sides of trapezoid
    lichobeznik-stredni_pricka_3 In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
  11. Reference angle
    anglemeter Find the reference angle of each angle:
  12. Cosine
    cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
  13. ABCD
    trig_1 AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
  14. Angles by cosine law
    357_triangle Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
  15. Angles
    triangle_1111_1 In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
  16. Triangle P2
    1right_triangle Can triangle have two right angles?
  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?