Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current height of the nearby Mikerinovi pyramid which at the same time throws a shadow 35.8 m long.

Correct answer:

a =  136.4343 m
b =  61.9841 m

Step-by-step explanation:

$$\begin{gathered} h=137.3\text{ m } \\ s=79.3\text{ m } \\ k=h\mathrm{/}s=137.3\mathrm{/}79.3={\displaystyle \frac{1373}{793}}\doteq 1.7314 \\ \alpha =180\mathrm{/}\pi \cdot \arctan (h\mathrm{/}s)=180\mathrm{/}3.1416\cdot \arctan (137.3\mathrm{/}79.3)\doteq 59.9907\text{ ° } \\ a=k\cdot 78.8=1.7314\cdot 78.8=136.4343\text{ m} \end{gathered}$$

$b=k\cdot 35.8=1.7314\cdot 35.8=61.9841\text{ m}$

Try another example

Related math problems and questions:

• Shadow
  A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house?
• 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.
• Mast
  Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'.
• Shadow and light
  Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
• Building
  How high is the building that throws horizontal shadow 85.6 m long at angle 34°12'?
• Tree shadow
  The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
• Powerplant chimney
  From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
• Reflector
  Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
• Tower's view
  From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church.
• The chimney
  The chimney casts a shadow 45 meters long. The one-meter-long rod standing perpendicular to the ground has a shadow 90 cm long. Calculate the height of the chimney.
• Tree shadow
  Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• 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°.
• Vertical rod
  The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time.
• A boy
  A boy of height 1.7m is standing 30m away from the flagstaff on the same level ground. He observes that the angle of deviation of the top of flagstaff is 30 degrees. Calculate the height of flagstaff.
• Calculate
  Calculate the area of triangle ABC, if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
• Triangle SAA
  The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.