A person is standing exactly 36 ft from a telephone pole. there is a 30° angle of elevation from the ground to the top of the pole. what is the height of the pole? 12 ft ft 18 ft ft

Answer:As per the statement:A person is standing exactly 36 ft from a telephone pole. there is a 30° angle of elevation from the ground to the top of the pole.⇒Distance of a person from the telephone pole = 36 ft.and angle of elevation ( [tex]\theta[/tex]) = 30 degree.We have to find the height of the pole.Let h be the height of the pole.Using tangent ratio:[tex]\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}[/tex]Here,Opposite side = h footAdjacent side = 36 ftAngle of elevation: [tex]\theta = 30^{\circ}[/tex]Substitute these to solve for AB:[tex]\tan 30^{\circ} = \frac{h}{36}[/tex]or[tex]h = 36\cdot \tan 30^{\circ}[/tex]or[tex]h = 36\cdot \frac{1}{\sqrt{3}}[/tex]Simplify:[tex]h = 12\sqrt{3}[/tex] ftTherefore, the height of the pole is [tex]12\sqrt{3}[/tex] ft