Question

1. determine the length of mn to the nearest tenth of an centimetre. 6. determine the length of xy to the nearest tenth of a centimetre. a. 36.9 cm b. 41.4 cm c. 8.5 cm d. 16.8 cm 7. determine the length of de to the nearest tenth of a centimetre. a. 8.4 cm b. 15.2 cm c. 31.4 cm d. 19.9 cm

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle DEF, we know an angle $\angle E = 29^{\circ}$ and the adjacent side $EF = 7.7$ cm, and we want to find the hypotenuse $DE$. We use the cosine ratio $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos E=\frac{EF}{DE}$.

Step2: Rearrange the formula to solve for DE

We can rewrite the formula as $DE=\frac{EF}{\cos E}$. Substituting $EF = 7.7$ cm and $E = 29^{\circ}$, and knowing that $\cos29^{\circ}\approx0.8746$, we have $DE=\frac{7.7}{\cos29^{\circ}}=\frac{7.7}{0.8746}\approx8.8$ cm.

Answer:

a. 8.8 cm