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



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
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:

  • Right triangle trigonometrics
    triangle2 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)
  • Right angled triangle 3
    right_triangle_3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
  • Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  • Trigonometric functions
    trigonom In the right triangle is: ? Find the value of s and c: ? ?
  • 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.
  • Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter, and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  • Right triangle
    rt_ttt A right triangle ABC is given, c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees.
  • Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  • Right triangle
    rt_triangle It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
  • Angles by cosine law
    357_triangle Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
  • Right angle
    rt_triangle_1 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.
  • Mast
    stoziar 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'.
  • Tetrahedral pyramid
    ihlan 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´.
  • Elevation angles
    mountain From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
  • Road
    12perctent The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
  • Ratio in trapezium
    lichobeznik_1 The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
  • Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.