Question

1. determine the length of side a to the nearest tenth of a centimetre.

a. 23.0 cm
b. 11.2 cm
c. 20.7 cm
d. 4.9 cm

Explanation:

Step1: Identify trigonometric relation

In right - triangle $DEF$ with right - angle at $E$, we know an angle $\angle D = 26^{\circ}$ and the adjacent side to $\angle D$ is $DE = 10.1$ cm. We want to find the opposite side $EF=a$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan D=\frac{a}{DE}$.

Step2: Substitute values and solve

We know that $\tan(26^{\circ})\approx0.4877$ and $DE = 10.1$ cm. Substituting into the formula $\tan D=\frac{a}{DE}$, we get $a = DE\times\tan D$. So, $a=10.1\times\tan(26^{\circ})$. Then $a = 10.1\times0.4877\approx4.9$ cm.

Answer:

d. $4.9$ cm