Viewing angle

The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure.
How far is the observer from the other end of the enclosure?

Correct answer:

c1 =  119.9416 m
c2 =  56.7276 m

Step-by-step explanation:

a=60 m A=30 b=102 m  a2=b2+c22 b c cos(A)  k=2 b cosA=2 b cos30 =2 102 cos30 =2 102 0.866025=176.66918 m  a2=b2+c2kc  602=1022+c2176.669182372 c c2+176.669c6804=0 c2176.669c+6804=0  p=1;q=176.669;r=6804 D=q24pr=176.6692416804=3995.99999999 D>0  c1,2=q±D2p=176.67±39962 c1,2=88.33459119±31.6069612585 c1=119.941552445=119.9416 m c2=56.7276299275   Factored form of the equation:  (c119.941552445)(c56.7276299275)=0

Our quadratic equation calculator calculates it.


Try calculation via our triangle calculator.




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






avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
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

Related math problems and questions:

  • Observer
    ohrada The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence?
  • 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?
  • SSA and geometry
    ssu_veta The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
  • The angle of view
    pole_1 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.
  • Two chords
    ssa From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
  • Inner angles
    triangle_1111 The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
  • 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.
  • Triangle's centroid
    triangles_1 In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
  • Children playground
    lich_5 The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles.
  • Mast shadow
    horizons Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
  • Water channel
    trapezium_prism_2 The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo
  • 30-60-90
    30-60-90 The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
  • Triangle SAS
    triangle_iron Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  • Triangle from median
    triangles_1 Calculate the perimeter, content, and magnitudes of the triangle ABC's remaining angles, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
  • Quadrilateral oblique prism
    kosyHranol What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
  • Two boats
    ship_1 Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.
  • Aircraft bearing
    aircraft-02_1 Two aircraft will depart from the airport at the same time, the first with a course of 30° and the second with a course of 86°. Both fly at 330 km/h. How far apart will they be in 45 minutes of flight?