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Find the value of x, round your answer to the nearest tenth.

Find the value of x, round your answer to the nearest tenth.-example-1

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11 votes

Answer:


\boxed {\boxed {\sf x \approx 3.7}}

Explanation:

Since we are given a right triangle, we can use the trigonometric ratios.

  • sin(θ)=opposite/hypotenuse
  • cos(θ)= adjacent/hypotenuse
  • tan(θ)=opposite/adjacent

We have the angle 24 and the sides 9 and x. 9 is the hypotenuse because it's opposite the right angle. x is the opposite, because it as across from the 24 degree angle. So, we have:

  • hypotenuse= 9
  • opposite=x

Therefore, we must use sine.


sin(24)= (x)/(9)

We are trying to solve for the value of x, so we must isolate the variable. x is being divided by 9. The inverse of division is multiplication. Multiply both sides by 9.


9*sin(24)= (x)/(9)*9


9*sin(24)=x


9*0.406736643=x


3.66062979=x

Round to the nearest tenth. The 6 in the hundredth place tells us to round the 6 to a 7.


3.7 \approx x

x is approximately 3.7

User Wyll Sales
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