# Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.

Result

a =  21
b =  20
c =  29
A =  46.397 °
B =  43.603 °
C =  90 °

#### Solution:

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$b = 2 \cdot \ S/a = 2 \cdot \ 210/21 = 20 \ \\ b = a_{ 2 } = 20$
$c = \sqrt{ a^2+b^2 } = \sqrt{ 21^2+20^2 } = 29$
$A = \dfrac{ 180^\circ }{ \pi } \cdot \arcsin(a/c) = \dfrac{ 180^\circ }{ \pi } \cdot \arcsin(21/29) \doteq 46.3972 = 46.397 ^\circ = 46^\circ 23'50"$
$B = \dfrac{ 180^\circ }{ \pi } \cdot \arcsin(b/c) = \dfrac{ 180^\circ }{ \pi } \cdot \arcsin(20/29) \doteq 43.6028 = 43.603 ^\circ = 43^\circ 36'10"$
$C = 90 = 90 ^\circ$

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#### Following knowledge from mathematics are needed to solve this word math problem:

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? Pythagorean theorem is the base for the right triangle calculator. Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

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