Answer:
Step-by-step explanation:
in the given triangle . one angle is 90 degree and other angle = 30
therefore third angle = 180 - 120 ( angle sum property of a triangle)
third angle = 60 degree
sin 30 = 5 / x (1)
cos 30 =third side /x (2)
from 1 * 2 we get ,
SIN 30 * COS 30 = 5/X * THIRD SIDE / X
1/2 *[tex]\sqrt{3}[/tex]/2 = 5 * THIRD SIDE / X^2
[tex]\sqrt{3}[/tex] * X^2/10 = THIRD SIDE
BY APPLYING PYTHAGORUS THEOREM
X^2 = 5^2 + [ [tex]\sqrt{3}[/tex] * X^2/10]^2
X^2 = 25 + 3x^4/100
x = square root of 25 + 3x^4/100 = 5+[tex]\sqrt{3}[/tex]x^2/10
x= 5+ [tex]\sqrt{3}[/tex] * x^2/10
