The side lengths of the triangle are x = 12.375 cm , y = 8.475 cm .
What is trigonometric ratio?
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 the triangle r = 15 cm
Perpendicular for ∠ θ = y
Base for ∠ θ = x
sin(θ)=0.565
cos(θ)=0.825
Now, using trigonometric ratio
sin θ = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
sin(θ)=0.565 (given)
0.565 = [tex]\frac{y}{r}[/tex]
0.565 * r = y
y = 0.565 * 15
y = 8.475 cm
cos θ = [tex]\frac{Base}{Hypotenuse}[/tex]
cos(θ)=0.825
0.825 = [tex]\frac{x}{r}[/tex]
0.825 * r = x
x = 0.825 * 15
x = 12.375 cm
Hence, the side lengths of the triangle are x = 12.375 cm , y = 8.475 cm.
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