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:
- \(\sin\theta=\dfrac{\text{opposite}}{\text{hypotenuse}}\)
- \(\cos\theta=\dfrac{\text{adjacent}}{\text{hypotenuse}}\)
- \(\tan\theta=\dfrac{\text{opposite}}{\text{adjacent}}\)
↓↓↓
\(\sin D = \dfrac{13}{26} = \dfrac{1}{2}\)
\(\sin E = \dfrac{13\sqrt{3}}{26} = \dfrac{\sqrt3}{2}\)
\(\cos D = \dfrac{13\sqrt3}{26} = \dfrac{\sqrt{3}}{2}\)
\(\cos E = \dfrac{13}{26} = \dfrac{1}{2}\)
Notice how cos(D) = sin(E) and cos(E) = sin(D) because E and D are opposite angles.
