Answer :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf x \approx 41}}}[/tex]

Step-by-step explanation:

Remember the three trigonometric ratios:

  • sinθ= opposite/hypotenuse
  • cosθ=adjacent/hypotenuse
  • tanθ=opposite/adjacent

Examine the triangle. We have an angle measuring 59°.

The side measuring 35 is opposite the angle. x is the hypotenuse because it is the longest side.

Since we have the opposite side and the hypotenuse, we use sine.

[tex]sin \theta= \frac {opposite}{hypotenuse}[/tex]

[tex]sin 59=\frac{35}{x}[/tex]

Now, solve for x by isolating the variable. We can cross multiply.  Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator.

[tex]\frac {sin59}{1}=\frac{35}{x}[/tex]

[tex]sin59*x=35*1 \\[/tex]

[tex]sin59*x=35[/tex]

x is being multiplied by sin 59. The inverse of multiplication is division. Divide both sides by sin59.

[tex]\frac {sin59*x}{sin59}=\frac {35}{sin59}[/tex]

[tex]x= \frac {35}{0.8571673007} \\[/tex]

[tex]x=40.8321689[/tex]

Let's round to the nearest whole number.

  • 40.8321689

The 8 in the tenths place tells us to the 0 to a 1.

[tex]x \approx 41[/tex]

The hypotenuse of the triangle is approximately 41.

BasketballEinstein

Answer:

[tex]\displaystyle 41 \approx x[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{35} = csc\:59 \hookrightarrow 35csc\:59 = x; 40,832168903... = x \\ \\ \boxed{41 \approx x}[/tex]

OR

[tex]\displaystyle \frac{35}{x} = sin\:59 \hookrightarrow xsin\:59 = 35 \hookrightarrow \frac{35}{sin\:59} = x; 40,832168903... = x \\ \\ \boxed{41 \approx x}[/tex]

Information on trigonometric ratios

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]

I am joyous to assist you at any time.

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