[tex]x=5.7[/tex], [tex]y=9.4[/tex] and ∠[tex]H[/tex][tex]=31[/tex]° is the solution of the triangle.
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
What is the sum of angle of triangle?
The sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn)
According to question,
In Δ FGH ,
∠G = 59°
Hypotenuse of triangle = 11
Base of triangle according to the ∠G = x
Perpendicular of triangle according to the ∠G = y
Now,
Cosθ = [tex]\frac{Base}{Hypotenuse}[/tex]
[tex]Cos[/tex] 59° = [tex]\frac{x}{11}[/tex]
[tex]x[/tex] [tex]=11[/tex]× [tex]0.515[/tex] ( Cos59° = [tex]0.515[/tex] )
x [tex]=5.7[/tex]
Sinθ = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]Sin[/tex] [tex]59[/tex]° [tex]=\frac{y}{11}[/tex]
[tex]y=11[/tex] * 0.857
y [tex]=9.4[/tex]
According to the sum of angle of triangle
∠F + ∠G +∠H = 180°
90° + 59° + ∠H = 180°
∠H = 180° - 90 -59
∠H = 31°
Hence,[tex]x=5.7[/tex], [tex]y=9.4[/tex] and ∠[tex]H[/tex][tex]=31[/tex]° is the solution of the triangle.
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