Right

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

3a+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=4.9−4b3  (4.9−4b)232+b2=1 (4.9−4b)2+32b2=32   25b2−39.2b+15.01=0  p=25;q=−39.2;r=15.01 D=q2−4pr=39.22−4⋅25⋅15.01=35.64 D>0  b1,2=−q±D2p=39.2±35.6450 b1,2=0.784±0.119398492453 b1=0.903398492453 b2=0.664601507547   Factored form of the equation:  25(b−0.903398492453)(b−0.664601507547)=0   α=arcsin⁡b=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 0.119398492453 \ \\ b_{1} = 0.903398492453 \ \\ b_{2} = 0.664601507547 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 25 (b -0.903398492453) (b -0.664601507547) = 0 \ \\ \ \\ \ \\ \alpha = \arcsin b = 64.6 ^\circ
β=arccos⁡b=25.4∘
γ=90∘

Try another example


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.

You need to know the following knowledge to solve this word math problem:


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

Next similar math problems:

  • Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  • Sailboat
    Plachetnice The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
  • Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  • Sphere in cone
    sphere_in_cone A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
  • 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.
  • Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  • 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.
  • River
    river From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
  • 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´.
  • Triangle in a square
    stvorec In a square ABCD with side a = 6 cm, point E is the center of side AB and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
  • Right triangle
    righttriangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
  • Space diagonal angles
    kvadr_diagonal Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
  • Cosine
    theta Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
  • R triangle
    right_triangle_1 Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
  • Square pyramid
    pyramid_4 Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
  • 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.
  • Sides of right angled triangle
    triangle_rt1 One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.