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PLEASE HELP!! I keep getting 1/2 (which is right) and squared root of 3 over 2 (which is wrong)

Find $\sin\ D$ , $\sin\ E$ , $\cos\ D$ , and $\cos\ E$ . Write each answer as a fraction in simplest form.

A right-angled triangle D F E, angle F marked right angle, hypotenuse D E marked 26, shortest side D F labeled 13 and second side F E labeled 13 square root of 3.



Answer :

Intriguing456

Answer and Explanation:

We are given a right triangle DFE where:

  • the right angle is angle F
  • the hypotenuse, DE, is 26
  • the short leg, DF, is 13
  • the long leg, FE, is 13√3

First, we should draw a diagram (see the attached image).

Next, we can formulate the trigonometric ratios we are solving for:

  • [tex]\sin\theta=\dfrac{\text{opposite}}{\text{hypotenuse}}[/tex]
  • [tex]\cos\theta=\dfrac{\text{adjacent}}{\text{hypotenuse}}[/tex]
  • [tex]\tan\theta=\dfrac{\text{opposite}}{\text{adjacent}}[/tex]

↓↓↓

[tex]\sin D = \dfrac{13}{26} = \dfrac{1}{2}[/tex]

[tex]\sin E = \dfrac{13\sqrt{3}}{26} = \dfrac{\sqrt3}{2}[/tex]

[tex]\cos D = \dfrac{13\sqrt3}{26} = \dfrac{\sqrt{3}}{2}[/tex]

[tex]\cos E = \dfrac{13}{26} = \dfrac{1}{2}[/tex]

Notice how cos(D) = sin(E) and cos(E) = sin(D) because E and D are opposite angles.

View image Intriguing456

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