Question

Can someone please help me find the answer to the following?

Answer 1

1077.19 ft

Step-by-step explanation:

Using the depression angle, we get that one of the angles of the formed triangle is also 18° because they are alternate interior angles, so we get:

Now, we can relate the distance x, the angle of 18°, and the height of the tower using the trigonometric function tangent, so:

`\begin{gathered} \tan 18=(Opposite)/(Adjacent) \\ \tan 18=(350)/(x) \end{gathered}`

Now, solving for x, we get:

`\begin{gathered} x\cdot\tan 18=x\cdot(350)/(x) \\ x\cdot\tan 18=350 \\ (x\cdot\tan18)/(\tan18)=(350)/(\tan 18) \\ x=(350)/(\tan 18) \end{gathered}`

Using the calculator, we get that tan(18) = 0.325, so x is equal to:

`x=(350)/(0.325)=1077.19\text{ }ft`

Therefore, the forest ranger is at 1077.19 ft from the fire.