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.

Result

a =  5.18 cm

Solution:

Solution in text a =

Try calculation via our triangle calculator.








Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




To solve this verbal math problem are needed these knowledge from mathematics:

Cosine rule uses trigonometric SAS triangle calculator. See also our trigonometric triangle calculator.

Next similar examples:

  1. Rhomboid
    triangle-ssa The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC?
  2. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  3. Sines
    sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
  4. Centre of mass
    centre_g_triangle The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
  5. Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
  6. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  7. Candy - MO
    cukriky_4 Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles triang
  8. Theorem prove
    thales_1 We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  9. Trigonometry
    sinus Is true equality? ?
  10. PIN - codes
    pin How many five-digit PIN - code can we create using the even numbers?
  11. Line
    skew_lines It is true that the lines that do not intersect are parallel?
  12. Sequence 2
    seq2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1
  13. AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  14. Average
    chart If the average(arithmetic mean) of three numbers x,y,z is 50. What is the average of there numbers (3x +10), (3y +10), (3z+10) ?
  15. Teams
    football_team How many ways can divide 16 players into two teams of 8 member?
  16. Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  17. Examination
    examination The class is 21 students. How many ways can choose two to examination?