# 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 result:

gb =  36 m
gt =  81 m

#### Solution:

$g_b+g_t=117 \ \\ g_b \cdot g_t = 54^2 \ \\ \ \\ g^2 -117g +2916 =0 \ \\ \ \\ a=1; b=-117; c=2916 \ \\ D = b^2 - 4ac = 117^2 - 4\cdot 1 \cdot 2916 = 2025 \ \\ D>0 \ \\ \ \\ g_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 117 \pm \sqrt{ 2025 } }{ 2 } \ \\ g_{1,2} = \dfrac{ 117 \pm 45 }{ 2 } \ \\ g_{1,2} = 58.5 \pm 22.5 \ \\ g_{1} = 81 \ \\ g_{2} = 36 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (g -81) (g -36) = 0 \ \\ \ \\ \ \\ g_b=36 \ \text{m}$
$g_t = 81 \ \text{m}$

Try calculation via our triangle calculator.

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:

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 quadratic equation?
See also our 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:

## Next similar math problems:

• Soccer balls
Pupils in one class want to buy two soccer balls together. If each of them brings 12.50 euros, they will miss 100 euros, if each brings 16 euros, they will remain 12 euros. How many students are in the class?
• Railway embankment
The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
• Find the 13
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
• An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
• Three parallels
The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
• Sides of right angled triangle
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.
• Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2
• Two chords
Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
• Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle?
• AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
• Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
• Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
• Solid cuboid
A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
• A bridge
A bridge over a river has the shape of the arc with bases of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. How wide is the ri
• Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.
• Diagonal 20
Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?