Answer :

theleangreenbean

Basic Trigonometric Ratios

We can name the sides of a right triangle by finding their location given one of the angles.

  • The "hypotenuse" is the longest side of a right triangle. It is opposite the right angle.
  • The "opposite" is the side that the angle does not touch.
  • The "adjacent" is the side that the angle does touch, that is not the hypotenuse.

The sine, cosine, and tangent ratios are the three basic trigonometric ratios:

  • The sine ratio: [tex]\sin\theta=\dfrac{opposite}{hypotenuse}[/tex]
  • The cosine ratio: [tex]\cos\theta=\dfrac{adjacent}{hypotenuse}[/tex]
  • The tangent ratio: [tex]\tan\theta=\dfrac{opposite}{adjacent}[/tex]

Solving the Question

The given angle in this case ([tex]\theta[/tex]) is the angle that measures 15°.

We're also given the side adjacent to it (that is not the hypotenuse), which measures 300 units.

And finally, we're asked to solve for the side opposite the given angle.

The ratio that involves solving using the opposite and the adjacent sides is the tangent ratio. Plug in all the given values:

[tex]\tan\theta =\dfrac{opposite}{adjacent}\\\\\tan(15^\circ)=\dfrac{x}{300}[/tex]

Isolate x by multiplying both sides by 300:

[tex]300\tan(15^\circ)=x\\\\300\tan(15^\circ)=80.4[/tex]

Therefore, x = 80.4 when rounded to the nearest tenth.

Answer

x = 80.4

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