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You can use tangent trigonometric ratio since that deals with perpendicular and base and since the case is related physically to the right triangle, thus it would be useful here.
The height of the roof is [tex]5\sqrt{2}\\\\[/tex] , the correct option is B.
Given
A right triangle is shown.
An altitude is drawn from the right angle to the opposite side to form another right angle.
The length of the altitude is h.
The length of one of the sides is 10.
Since the triangle is isosceles, hence the base angles will be 45 degrees.
Therefore,
The height of the roof is;
[tex]\rm Cos 45=\dfrac{Base}{Hypotenuse}\\\\Cos45=\dfrac{h}{10}\\\\h = 10 \times cos45'\\\\h=10\times \dfrac{1}{\sqrt{2} }\\\\h = 5 \times \sqrt{2} \times \sqrt{2} \times \dfrac{1}{\sqrt{2}}\\\\h=5 \times \sqrt{2} \\\\h=5 \sqrt{2}[/tex]
Hence, the height of the roof is [tex]5\sqrt{2}\\\\[/tex] .
To learn more about the Isosceles triangle click the link given below.
https://brainly.com/question/20734777