Question

trigonometric ratios which trigonometric ratios are correct for triangle def? choose three correct answers. sin (d) = 24/25 tan (d) = 7/24 tan (d) = 24/7

Explanation:

1. Recall the definitions of trigonometric - ratios:

• In a right - triangle, for an acute angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\).
• Assume that in right - triangle \(DEF\), if the side opposite to angle \(D\) is \(24\) and the side adjacent to angle \(D\) is \(7\), then by the Pythagorean theorem, the hypotenuse \(h=\sqrt{24^{2}+7^{2}}=\sqrt{576 + 49}=\sqrt{625}=25\).

1. Calculate \(\sin(D)\):

• \(\sin(D)=\frac{\text{opposite to }D}{\text{hypotenuse}}\). If the opposite side to \(D\) is \(24\) and the hypotenuse is \(25\), then \(\sin(D)=\frac{24}{25}\).

1. Calculate \(\tan(D)\):

• \(\tan(D)=\frac{\text{opposite to }D}{\text{adjacent to }D}\). If the opposite side to \(D\) is \(24\) and the adjacent side to \(D\) is \(7\), then \(\tan(D)=\frac{24}{7}\).

Answer:

The correct answers are \(\sin(D)=\frac{24}{25}\) and \(\tan(D)=\frac{24}{7}\). So the selected options are the ones with \(\sin(D)=\frac{24}{25}\) and \(\tan(D)=\frac{24}{7}\) (assuming the options are as presented in the image where the first option has \(\sin(D)=\frac{24}{25}\) and the third option has \(\tan(D)=\frac{24}{7}\)).