Question

A honeybee sitting on a tulip wanted to fly to a daffodil located 100 meters due east. Although the honeybee flew in a straight line, it mistakenly flew in a direction 5° south of east. When the bee was directly south of the daffodil, how many meters from the bee was the daffodil? Enter your answer to 2 decimal places.

Answer 1

Let's begin by listing out the given information:

Let the initial location of the honeybee be represented as B

Let the location of the honeybee be represented as C

Let the location of the daffodil be represented as D

`\begin{gathered} BC(adjacent)=100m \\ \angle B=5^(\circ) \\ CD(opposite)=? \end{gathered}`

We will calculate for CD using the Trigonometric ratio (SOHCAHTOA). We will use TOA:

`\begin{gathered} Tan\theta=(opposite)/(adjacent)=(CD)/(BD) \\ \theta=5^(\circ),BD=100m \\ Tan5^(\circ)=(CD)/(100) \\ CD=100\cdot Tan5^(\circ) \\ CD=8.78\approx8.8 \\ CD=8.8m \end{gathered}`