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 result:

c₁ =  119.9416 m
c₂ =  56.7276 m

Solution:

$$\begin{gathered} a=60\text{ m } \\ A=30^{\circ } \\ b=102\text{ m } \\ {a}^2=b^2+c^2-2\cdot b\cdot c\cdot \cos (A) \\ k=2\cdot b\cdot \cos A^{\circ }=2\cdot b\cdot \cos 30^{\circ }=2\cdot 102\cdot \cos 30^{\circ }=2\cdot 102\cdot 0.866025=176.66918\text{ m } \\ {a}^2=b^2+c^2-k\ast c \\ 60^2=102^2+c^2-176.669182372\cdot c \\ -c^2+176.669c-6804=0 \\ {c}^2-176.669c+6804=0 \\ p=1;q=-176.669;r=6804 \\ D=q^2-4pr=176.669^2-4\cdot 1\cdot 6804=3995.99999999 \\ D>0 \\ {c}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{176.67\pm \sqrt{3996}}{2}} \\ {c}_{1,2}=88.33459119\pm 31.6069612585 \\ {c}_1=119.941552445=119.9416\text{ m } \\ {c}_2=56.7276299275 \\ \text{ Factored form of the equation: } \\ (c-119.941552445)(c-56.7276299275)=0 \end{gathered}$$

Our quadratic equation calculator calculates it.


Try calculation via our triangle calculator.

Try another example

Showing 0 comments:

Next similar math problems:

• Observer
  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
  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
  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
  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
  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
  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
  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.
• Children playground
  The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
• Mast shadow
  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
  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
  The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
• Triangle SAS
  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
  Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
• Two boats
  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.
• Quadrilateral oblique prism
  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°.
• Elevation angles
  From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
• Internal angles
  The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete