Question

What is the height of the antenna round to hundredths

Answer 1

Step 1

State the ratio from SOHCAHTOA that can be used to find the height of the antenna to the nearest hundredth

$\tan \theta=\frac{opposite}{\text{adjacent}}$

Where;

$\begin{gathered} \theta=53^{\circ} \\ \text{opposite = height of antenna} \\ \text{adjacent = 15m} \end{gathered}$

Step 2

Find the height of the antenna rounded to the hundredths

$\begin{gathered} \tan \text{ 53=}\frac{height\text{ of antenna}}{15} \\ \text{height of antenna = tan53}\times15 \\ \text{height of antenna = 19.90567232}m \\ \text{height of antenna }\approx\text{ 19.91m to the nearest hundredths} \end{gathered}$

Hence, the height of the antenna rounded to the nearest hundredths = 19.91m