Question

1. 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

a. 8.8 cm
b. 15.9 cm
c. 3.7 cm
d. 13.9 cm

Explanation:

Step1: Identify trig - ratio

In right - triangle $\triangle DEF$ with right - angle at $F$, we know the side $DF = 7.7$ cm and we want to find the hypotenuse $DE$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 29^{\circ}$ and the adjacent side to $\angle E$ is $DF$. So, $\cos E=\frac{DF}{DE}$.

Step2: Rearrange the formula

We can rewrite the formula $\cos E=\frac{DF}{DE}$ as $DE=\frac{DF}{\cos E}$. Substituting $\angle E = 29^{\circ}$ and $DF = 7.7$ cm, we have $DE=\frac{7.7}{\cos29^{\circ}}$.

Step3: Calculate the value

We know that $\cos29^{\circ}\approx0.8746$. Then $DE=\frac{7.7}{0.8746}\approx8.8$ cm.

Answer:

a. 8.8 cm