Question

A tent guy line supports one of the upright tent poles. It runs from the top of the pole to a peg in the ground two and a half metres away from the base of the pole. If the guy line is 359cm long, how tall is the upright tent pole? Give your answer in centimetres correct to the nearest centimetre.

Answer 1

Answer:

258 cm

Step-by-step explanation:

Given:

Distance from the base of the pole to the base of a tent guy line is $2\frac{1}{2}$

Length of a tent guy line is 359 cm

To find: Height of the upright tent pole

Solution:

Let AB denotes the pole and AC denotes a tent guy line.

According to Pythagoras theorem, in a right angled triangle, square of hypotenuse is equal to sum of squares of other two sides.

$AC^2=AB^2+BC^2$

$AC=359 cm\\AB=x\\BC=2\frac{1}{2}\,m=\frac{5}{2}\,m=\frac{5}{2}\times 100=250\,cm$

Therefore,

$(359)^2=x^2+(250)^2\\128881=x^2+62500\\128881-62500=x^2\\66381=x^2\\x=257.6\,cm\approx 258\,cm$

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