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Find the value of x and y rounded to the nearest tenth.

a. x=48.1,y=46.4
b. x=48.1,y=139.3
c. x=24.0,y=139.3
d. x=24.0,y=46.4

Find the value of x and y rounded to the nearest tenth a x481y464 b x481y1393 c x240y1393 d x240y464 class=

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Answer:

(D)

Step-by-step explanation:

From the given figure, we have

AB=34 and AD=x and BD=y.

Since, ∠D=45° and ∠B=30°, therefore using the angle sum property, we have

∠A+∠B+∠D=180°

⇒∠A+45+30=180

⇒∠A=105°

Now, using the sine formula, we have

[tex]\frac{x}{sin30^{\circ}}=\frac{34}{sin45^{\circ}}[/tex]

⇒[tex]x=\frac{34{\times}sin30^{\circ}}{sin45^{\circ}}[/tex]

⇒[tex]x=\frac{34\sqrt{2}}{2}[/tex]

⇒[tex]x=24.0[/tex]

And, [tex]\frac{y}{sin105^{\circ}}=\frac{34}{sin45^{\circ}}[/tex]

⇒ [tex]y=\frac{34{\times}sin105^{\circ}}{sin45^{\circ}}[/tex]

⇒[tex]y=\frac{34{\times}0.965}{0.707}[/tex]

⇒[tex]y=46.4[/tex]

Therefore, the values of x and y are 24 and 46.4 respectively.

Thus, option D is correct.

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The value of x and y in the ΔABC is 24 and 46.4.

Given to us

AC = 34

∠B = 45°

∠C = 30°

What are the basic Trigonometric functions?

[tex]Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

What is the length of the perpendicular in ΔABC?

In ΔADC

[tex]Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin (\angle C)=\dfrac{AD}{AC}[/tex]

[tex]Sin (30^o)=\dfrac{AD}{34}\\\\AD = 17[/tex]

[tex]Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]Cos (\angle C)=\dfrac{DC}{AC}[/tex]

[tex]Cos (30^o)=\dfrac{DC}{34}\\\\DC = 29.44486[/tex]

What is the value of x?

In ΔABD

[tex]Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin (\angle B)=\dfrac{AD}{AB}[/tex]

[tex]Sin (45^o)=\dfrac{17}{x}\\\\x= 24.04\approx24.0[/tex]

[tex]Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]Tan (\angle B)=\dfrac{AD}{BD}[/tex]

[tex]Tan (45^o)=\dfrac{17}{BD}\\\\BD = 17[/tex]

What is the value of y?

We know that line BC is the sum of line BD and DC, therefore,

[tex]y = BC\\\\y= BD+DC\\\\y = 17+29.44486\\\\y = 46.44486[/tex]

Hence, the value of x and y in the ΔABC is 24 and 46.4.

Learn more about Trigonometric functions:

https://brainly.com/question/6904750

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