RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m.
How long are hypotenuse segments?

Correct answer:

gb =  36 m
gt =  81 m

Step-by-step explanation:

gb+gt=117 gbgt=542  g2117g+2916=0  a=1;b=117;c=2916 D=b24ac=1172412916=2025 D>0  g1,2=b±D2a=117±20252 g1,2=117±452 g1,2=58.5±22.5 g1=81 g2=36   Factored form of the equation:  (g81)(g36)=0   gb=36 m
gt=81 m

Try calculation via our triangle calculator.

Did you find an error or inaccuracy? Feel free to write us. Thank you!


Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

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

Related math problems and questions:

  • Hypotenuse - RT
    triangle_bac A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  • Right 24
    euclid_theorem 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.
  • Triangle KLM
    klm_triangle In the rectangular triangle KLM, where is hypotenuse m (sketch it!). Find the length of the leg k and the height of triangle h if the hypotenuse's segments are known MK = 5cm and ml = 15 cm.
  • 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.
  • Right isosceles triangle
    euclid_theorem Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
  • The sides
    rt_triangle The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle.
  • Hypotenuse and height
    euklides In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
  • Euclid1
    pravitko Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
  • Right angled triangle
    fun-triangle The hypotenuse of a right triangle is 17 cm long. When we decrease the length of legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs.
  • 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.
  • Right triangle Alef
    r_triangle The obvod of a right triangle is 84 cm, and the hypotenuse is 37 cm long. Determine the lengths of the legs.
  • Euclid theorems
    euklidova_veta_trojuhelnik_nakres Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
  • R triangle
    right_triangle Calculate the right triangle area whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
  • Altitude angles
    aircraft-02 Cities A, B, C lie in one elevation plane. C is 50 km east of B, B is north of A. C is deviated by 50° from A. The plane flies around places A, B, C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Find the altit
  • Right triangle - ratio
    rt_triangle The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
  • Difference of legs
    rt_triangle In a right triangle, the length of the hypotenuse is 65 m, and the difference of legs is 23 m. Calculate the perimeter of this triangle.
  • One leg
    rt_triangle One leg of a right triangle is 1 feet longer than the other leg. The hypotenuse is 5 feet. Find the lengths of the three sides of the triangle.