# Triangle and its heights

Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.

Result

a =  17.5 cm
b =  12.5 cm
c =  7.84 cm

#### Solution:

$\ \\ \sin \gamma = \dfrac{ v_a }{ b } = \dfrac{ v_b }{ a } \ \\ b = a - 5 \ \\ \ \\ a = \dfrac{ 5 \cdot 7 } { 7 - 5} = 17.5 \ \text{cm}$
$b = a - 5 = 12.5 \ \text{cm}$
$\ \\ \cos \gamma = \dfrac{ \sqrt{a^2 - v_b^2 } }{ a } \ \\ c = \sqrt{ a^2 + b^2 - 2ab \cos \gamma } = 7.84 \ \text{cm}$

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Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.

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