Question

1. determine the length of side d to the nearest tenth of a centimetre. a. 26.5 m b. 12.0 m c. 6.9 m d. 6.1 m

Explanation:

Step1: Identify the trigonometric relation

We know that in right - triangle $\triangle LMN$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 63^{\circ}$, the opposite side to $\theta$ is $LM = 13.5$ m and the adjacent side is $MN$ (which we want to find). So, $\tan63^{\circ}=\frac{LM}{MN}$.

Step2: Rearrange the formula to solve for $MN$

Since $\tan63^{\circ}\approx1.9626$ and $\tan63^{\circ}=\frac{13.5}{MN}$, we can rewrite the formula as $MN=\frac{13.5}{\tan63^{\circ}}$.

Step3: Calculate the value of $MN$

$MN=\frac{13.5}{1.9626}\approx6.9$ m.

Answer:

c. 6.9 m