The value of a and b is [tex]\frac{10}{\sqrt{2} }[/tex] .
What is trigonometric ratios?
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.
The basic trigonometric ratios formulas are given below,
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
cot θ = Base/Perpendicular
According to the question
Hypotenuse of right angle triangle = 10
Base of of right angle triangle = a
Perpendicular of right angle triangle = b
Now,
By using trigonometric ratios
sin θ = Perpendicular/Hypotenuse ---------(1)
substituting the values in equation (1)
sin 45° = [tex]\frac{b}{10}[/tex]
[tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{b}{10}[/tex]
b = [tex]\frac{10}{\sqrt{2} }[/tex]
cos θ = Base/Hypotenuse
cos 45° = [tex]\frac{a}{10}[/tex]
[tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{a}{10}[/tex]
a = [tex]\frac{10}{\sqrt{2} }[/tex]
Hence, The value of a and b is [tex]\frac{10}{\sqrt{2} }[/tex] .
To know more about trigonometric ratios here:
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