The staircase

The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.

Correct answer:

x =  8.2122 m

Step-by-step explanation:

$$\begin{gathered} h=3.6\text{ m } \\ \alpha =26\text{ ° } \\ \sin \alpha =h:x \\ x=h\mathrm{/}\sin \alpha \mathrm{°}=h\mathrm{/}\sin 26\mathrm{°}=3.6\mathrm{/}\sin 26\mathrm{°}=3.6\mathrm{/}0.438371=8.212=8.2122\text{ m} \end{gathered}$$

Try another example

Related math problems and questions:

• 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?
• Length of the chord
  Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°.
• Clouds
  Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
• A trapezoid
  A trapezoid with a base length of a = 36.6 cm, with angles α = 60°, β = 48° and the height of the trapezoid is 20 cm. Calculate the lengths of the other sides of the trapezoid.
• 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°?
• 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'.
• Right triangle trigonometrics
  Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
• The cable car
  The cable car is 2610 m long and rises at an angle of 35°. Calculate the height difference between the lower and upper station of the cable car.
• Building
  The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
• Right triangle
  Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
• Right angle
  In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
• Building
  How high is the building that throws horizontal shadow 85.6 m long at angle 34°12'?
• Right angled triangle 3
  Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
• Maple
  Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
• Diagonal
  The diagonal of the rectangle has a length of 41.4 cm. The angle between the diagonal and longer side of the rectangle is 26°. Calculate the area of the rectangle.
• The ladder
  The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
• Rhomboid
  Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°.