# Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17 m.

Result

a =  11.63 m
b =  17 m
c =  20.6 m

#### Solution:

$$\smash{ c_b^2 = b^2 - v^2 \\~\\c_b = \sqrt{ 17^2 - 9.6^2 } = 14.03 \\~\\ \\~\\v^2 = c_a c_b \\~\\c_a = v^2/ c_b = 9.6 / 14.03 = 6.57 \ m \\~\\ \\~\\c = c_a + c_b = 20.6 \ { m } \\~\\ \\~\\a^2+b^2 = c^2 \\~\\a = \sqrt{ c^2 - b^2} = \sqrt{ 20.6 \ { m } ^2 - 17^2} = 11.63 \ m \\~\\b= 17 \ m \\~\\c = 20.6 \ { m } }$$

Try calculation via our triangle calculator.

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### To solve this verbal math problem are needed these knowledge from mathematics:

Pythagorean theorem is the base for the right triangle calculator. See also our right triangle calculator. Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? See also our trigonometric triangle calculator.

## Next similar examples:

1. Without Euclid laws
Right triangle ABC with right angle at the C has a=10 and hypotenuse c=27. Calculate the height h of this triangle without the use of Euclidean laws.
2. Euclid2
In right triangle ABC with right angle at C is given side a=29 and height v=27. Calculate the perimeter of the triangle.
3. Euklid4
Legs of a right triangle have dimensions 61 m and 39 m. Calculate the length of the hypotenuse and the height of this right triangle.
4. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
5. Triangle KLM
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 hypotenuse's segments are known mk = 5cm and ml = 15cm
6. Hypotenuse and height
In a right triangle is length of the hypotenuse c = 45 cm and height hc = 19 cm. Determine the length of both trangle legs.
7. 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.
8. Catheti
The hypotenuse of a right triangle is 20 and the sum of legs is 28. Calculate the length of its legs.
9. Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
10. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
11. Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
12. ABS CN
Calculate the absolute value of complex number -14-7i.
13. Euclidean distance
Calculate the Euclidean distance between shops A, B and C, where: A 56 0.05 B 55 0.09 C 51 0.07 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
14. Theorem prove
We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
15. Calculation
How much is sum of square root of six and the square root of 441?