applications of trigonometry - An electrician wants to repair an electric connection on a pole of height 9 m. He needs to reach 1.8 m below the top of the pole to do repair work.

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Analyse the given information and Draw a figure.

GIVEN: The pole height AB = 9 m

Height of the electric pole to do repair = AB - BC = 9 - 1.8 = 7.2

Angle between the ladder and the ground = 60\degree

Length of the ladder = ?

The distance between the foot the ladder and foot of the pole AD = ?

Step 2: Find the length of the ladder by using the trigonometric ratios

NOTE: From right triangle ADC, we know the opposite side and we have to calculate the hypotenuse.

So take the \sin \theta = \frac{opposite}{hypotenuse}

EXAMPLE: \sin 60\degree = \frac{AC}{DC}

\frac{\sqrt{3}}{2} = \frac{7.2}{DC} ( \because \sin 60\degree = \frac{\sqrt{3}}{2} )

DC = \frac{2*7.2}{\sqrt{3}}

Simplify the above equation by Rationalizing

DC = \frac{2*7.2}{\sqrt{3}} \frac{\sqrt{3}}{\sqrt{3}}

DC = \frac{14.4*\sqrt{3}}{3}

DC = 4.8 * 1.732

DC = 8.3136 m

Height of the ladder = 8.3136 m

Step 3: Calculate the distance between the foot the ladder and foot of the pole by using the trigonometric ratios.

NOTE: From right triangle ADC, we know the opposite side and we have to calculate the adjacent side.

So take the \tan \theta = \frac{opposite}{hypotenuse}

EXAMPLE: \tan 60\degree = \frac{AC}{AD}

\sqrt{3} = \frac{7.2}{AD}

AD = \frac{7.2}{\sqrt{3}}

Simplify the above equation by Rationalizing

AD = \frac{7.2}{\sqrt{3}} \frac{\sqrt{3}}{\sqrt{3}}

AD = \frac{7.2*\sqrt{3}}{3}

AD = \frac{7.2*1.732}{3}

AD = 2.4 * 1.732

AD = 4.1568 m

The distance between the foot the ladder and foot of the pole = 4.1568 m