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}*15 \\ \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