Question

Two ropes, ad and bd, are tied to a peg on the ground at point

d. the other ends of the ropes are tied to points a and b on a flagpole, as shown below:two ropes, ad and bd, are tied to a peg on the ground at point

d. the other ends of the ropes are tied to points a and b on a flagpole. angle adb measures 60 degrees and angle bdc measures 30 degrees. the length of dc is 10 multiplied by square root of 3.angle adc measures 60° and angle bdc measures 30°. what is the distance between the points a and b on the flagpole?

Answer 1

Heya,

IN ∆BDC, <C = 90° , <D = 30°

now we can use trigonometry ratios there,

So, tan30° = BC/DC

1/√3 = BC/10√3

BC = 10√3/√3

BC = 10CM


AND,

IN ∆ ADC , <C = 90° , <D = 60°

So, tan60° = AC/DC

√3 = AC/10√3

AC = 10√3 * √3

AC = 10 * 3

AC = 30CM

NOW, THE DISTANCE BETWEEN A AND B ON THE PLAGPOLE AB = (AC - BC)

AB = (30 - 10)CM

AB = 20CM

HENCE,
THE DISTANCE BETWEEN A AND B ON THE PLAGPOLE AB = 20CM