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?

Correct answer:

x =  119.9 m

Step-by-step explanation:

$$\begin{gathered} {\displaystyle \frac{\sin \beta }{\sin 30^{\circ }}}={\displaystyle \frac{102}{60}} \\ \beta =\arcsin ({\displaystyle \frac{102}{60}}\cdot \sin 30^{\circ })=1.016=58^{\circ }12^{\mathrm{\prime }}42\mathrm{"} \\ \gamma =180^{\circ }-30^{\circ }-58^{\circ }12^{\mathrm{\prime }}42\mathrm{"}=91^{\circ }47^{\mathrm{\prime }}18\mathrm{"} \\ {\displaystyle \frac{\sin \gamma }{\sin \beta }}={\displaystyle \frac{x}{102}} \\ x=102\cdot {\displaystyle \frac{\sin \gamma }{\sin \beta }}=119.9\text{ m} \end{gathered}$$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• 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?
• 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.
• 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?
• 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.
• 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.
• TV tower
  Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°?
• 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.
• Two triangles SSA
  Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
• Bearing - navigation
  A ship travels 84 km on a bearing of 17° and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
• 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 °.
• Aircraft bearing
  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?
• 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
• Two forces
  Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer.
• 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?
• 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?