Question

14 in triangle mct, the measure of ∠t = 90°, mc = 85 cm, ct = 84 cm, and tm = 13 cm. which ratio represents the sine of ∠c? 1) \\( \frac { 13 } { 85 } \\) 2) \\( \frac { 84 } { 85 } \\) 3) \\( \frac { 13 } { 84 } \\) 4) \\( \frac { 84 } { 13 } \\)

Explanation:

Step1: Recall the sine ratio formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Identify the sides relative to \(\angle C\)

For \(\angle C\) in right - triangle \(MCT\) with \(\angle T = 90^{\circ}\), the side opposite to \(\angle C\) is \(TM\) and the hypotenuse is \(MC\).
Given \(TM = 13\mathrm{cm}\) and \(MC=85\mathrm{cm}\).

Step3: Calculate \(\sin C\)

Using the formula \(\sin C=\frac{TM}{MC}\), substituting the values we get \(\sin C=\frac{13}{85}\).

Answer:

1. \(\frac{13}{85}\)