Powerplant chimney

From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney?

Correct result:

x =  313.2801 m

Solution:

$$\begin{gathered} h_1=7.5\text{ m } \\ \alpha =76+30\mathrm{/}60={\displaystyle \frac{153}{2}}=76.5^{\circ } \\ \beta =5+50\mathrm{/}60={\displaystyle \frac{35}{6}}\doteq 5.8333^{\circ } \\ \tan \beta =h_1:v \\ v=h_1\mathrm{/}\tan {\beta }^{\circ }=h_1\mathrm{/}\tan 5.83333333333^{\circ }=7.5\mathrm{/}\tan 5.83333333333^{\circ }=7.5\mathrm{/}0.102164=73.4113 \\ \tan \alpha =h_2:v \\ {h}_2=v\cdot \tan {\alpha }^{\circ }=v\cdot \tan 76.5^{\circ }=73.4113\cdot \tan 76.5^{\circ }=73.4113\cdot 4.1653=305.78007 \\ x=h_1+h_2=7.5+305.7801=313.2801\text{ m} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Cone side
  Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
• 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
• The tower
  The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
• An observer
  An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
• 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.
• Traffic sign
  There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
• Tree
  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?
• Tetrahedral pyramid
  Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
• Sphere in cone
  A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
• The Eiffel Tower
  The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
• Observation tower
  From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower?
• Ratio iso triangle
  The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
• 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°?
• Fighter
  A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
• Four sided prism
  Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
• Octagonal pyramid
  Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
• Power line pole
  From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.