Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if:

3a+4b=4.9c3a +4b = 4.9c


Correct result:

α =  64.6 °
β =  25.4 °
γ =  90 °

Solution:

 3a+4b=4.9c  c=1 3a+4b=4.9 a2+b2=1  a=4.94b3  (4.94b)232+b2=1 (4.94b)2+32b2=32   25b239.2b+15.01=0  p=25;q=39.2;r=15.01 D=q24pr=39.2242515.01=35.64 D>0  b1,2=q±D2p=39.2±35.6450 b1,2=0.784±0.11939849245279 b1=0.90339849245279 b2=0.66460150754721   Factored form of the equation:  25(b0.90339849245279)(b0.66460150754721)=0   α=arcsinb=64.6 \ \\ 3a +4b = 4.9c \ \\ \ \\ c=1 \ \\ 3a +4b = 4.9 \ \\ a^2+b^2 =1 \ \\ \ \\ a=\dfrac{ 4.9 - 4 b}{ 3} \ \\ \ \\ \dfrac{ (4.9 - 4 b)^2}{ 3^2} + b^2 =1 \ \\ (4.9 - 4 b)^2 + 3^2 b^2 = 3^2 \ \\ \ \\ \ \\ 25b^2 -39.2b +15.01 =0 \ \\ \ \\ p=25; q=-39.2; r=15.01 \ \\ D = q^2 - 4pr = 39.2^2 - 4\cdot 25 \cdot 15.01 = 35.64 \ \\ D>0 \ \\ \ \\ b_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 39.2 \pm \sqrt{ 35.64 } }{ 50 } \ \\ b_{1,2} = 0.784 \pm 0.11939849245279 \ \\ b_{1} = 0.90339849245279 \ \\ b_{2} = 0.66460150754721 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 25 (b -0.90339849245279) (b -0.66460150754721) = 0 \ \\ \ \\ \ \\ \alpha = \arcsin b = 64.6 ^\circ
β=arccosb=25.4 \beta = \arccos b = 25.4 ^\circ
γ=90\gamma = 90 ^\circ



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


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

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




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Isosceles triangle 10
    iso_23 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
  • Maple
    tree_javor 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.
  • Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  • The right triangle
    rt_triangle_1 In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
  • Isosceles triangle
    rr_triangle2_1 Calculate the size of the interior angles and the length of the base of the isosceles triangle if the length of the arm is 17 cm and the height to the base is 12 cm.
  • One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  • Steeple
    church_tower Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
  • If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  • Building
    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?
  • The rescue helicopter
    helicopter The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?
  • Perimeter of triangle
    rt_triangle_1 In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
  • Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  • Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  • Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  • Trigonometry
    sinus Is true equality? ?