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Find x and explain how you found it!

Find X And Explain How You Found It class=

Sagot :

VirαtKσhli

Answer:

[tex]\Large\boxed{\sf x = 19.2}[/tex]

Step-by-step explanation:

Here a right angled triangle is given to us and we need to find out the value of x . The measure of one of the sides is 24 and one of the acute angle is 53° .

  • Here 24 is hypotenuse of the triangle and x is the perpendicular .

So here we may use the ratio of sine as ,

[tex]\sf\qquad\longrightarrow sin\theta =\dfrac{p}{h} \\\\[/tex]

• On substituting the respective values ,

[tex]\sf\qquad\longrightarrow sin53^\circ =\dfrac{x}{24}\\\\[/tex]

Substitute the value of sin 53° = 4/5 ,

[tex]\sf\qquad\longrightarrow \dfrac{4}{5}=\dfrac{x}{24} \\\\[/tex]

Cross multiply ,

[tex]\sf\qquad\longrightarrow x =\dfrac{24*4}{5} \\\\[/tex]

Simplify,

[tex]\sf\qquad\longrightarrow \frak{\pink{x =19.2}} \\\\[/tex]

[tex]\rule{200}4[/tex]

Here we use trigonometric ratios

[tex]\\ \rm\hookrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\hookrightarrow sin53=\dfrac{x}{24}[/tex]

[tex]\\ \rm\hookrightarrow 0.8(24)=x[/tex]

[tex]\\ \rm\hookrightarrow x=19.2[/tex]

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