Question

From the ground 18ft away from the tree, the angle of elevation to the top of the tree is 30°. Find the height, h, of the tree to the nearest foot. *Round the answer to the nearest foot*

Answer 1

As the problem can be modeled using a right triangle and the trigonometric functions of the inner angles.

The trigonometric function that relates the two sides of the triangle but not the hypotenuse is the tangent.

`\tan (30^(\prime))=(opp)/(adj)`

write the tan in function of the information given

`\tan (30)=(h)/(18)`

solve the equation for x

`\tan (30)=\frac{\sqrt[]{3}}{3}`

`\begin{gathered} \frac{\sqrt[]{3}}{3}=(h)/(18) \\ 18\cdot\frac{\sqrt[]{3}}{3}=h \\ 6\sqrt[]{3}=h \\ h=10.392\cong10ft \end{gathered}`