Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.

Correct result:

a =  6 cm
b =  6.708 cm
c =  9 cm

Solution:

$a=6\text{ cm}$

$c_{2}=5 \ \\ h/a=\sqrt{ c_{2}^2-h^2 }/h \ \\ h^2/a=\sqrt{ c_{2}^2-h^2 } \ \\ 5 \ \sqrt{ 36-h^2 }=h^2 \ \\ \ \\ h=2 \cdot \ \sqrt{ 5 }=2 \ \sqrt{ 5 } \doteq 4.4721 \ \\ b=\sqrt{ c_{2}^2+h^2 }=\sqrt{ 5^2+4.4721^2 }=3 \ \sqrt{ 5 }=6.708 \ \text{cm}$

$c=\sqrt{ a^2+b^2 }=\sqrt{ 6^2+6.7082^2 } \doteq 8.9998 \ \\ c_{1}=c-c_{2}=8.9998-5 \doteq 3.9998 \ \\ x_{1}=a^2-c \cdot \ c_{1}=6^2-8.9998 \cdot \ 3.9998 \doteq 0.002 \ \\ x_{2}=b^2-c \cdot \ c_{2}=6.7082^2-8.9998 \cdot \ 5 \doteq -0.002 \ \\ c=8.9998=9 \ \text{cm}$

Try calculation via our triangle calculator.

Try another example

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:

Next similar math problems:

• Euclid 5
  Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height v_c = 5 cm.
• Euclid2
  In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
• Calculate
  Calculate the length of a side of the equilateral triangle with an area of 50cm².
• RT triangle and height
  Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
• Catheti
  The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
• Triangle ABC
  In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
• Right 24
  Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
• Roots
  Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
• Equation 23
  Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
• Holidays - on pool
  Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
• Solve 3
  Solve quadratic equation: (6n+1) (4n-1) = 3n²
• Equation
  Equation ? has one root x₁ = 8. Determine the coefficient b and the second root x₂.
• The product
  The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
• Discriminant
  Determine the discriminant of the equation: ?
• Expression with powers
  If x-1/x=5, find the value of x⁴+1/x⁴
• Algebra
  X+y=5, find xy (find the product of x and y if x+y = 5)
• Evaluation of expressions
  If a²-3a+1=0, find (i)a²+1/a² (ii) a³+1/a³