trigonometry set up

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trigonometry set up

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To secure a 618-meter radio tower against high winds, guy wires are attached to a ring on the tower. The ring is 9 meters from the top. The wires form a 76^o angle with the ground. To the nearest hundredth meter find the length of the guy wire

Guest Jun 22, 2014

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You use the fact that the sine of an angle is opposite over hypotenuse here.

opposite = 618 - 9 = 609m

so sin(76°) = 609/h

h = 609/sin(76°)

${\mathtt{h}} = {\frac{{\mathtt{609}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{76}}^\circ\right)}}} \Rightarrow {\mathtt{h}} = {\mathtt{627.643\: \!700\: \!274\: \!085\: \!654\: \!1}}$

so h = 627.64m to the nearest hundredth of a meter.

Alan Jun 22, 2014

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Alan · Answer 1 · 2014-06-22T06:40:52

You use the fact that the sine of an angle is opposite over hypotenuse here.

opposite = 618 - 9 = 609m

so sin(76°) = 609/h

h = 609/sin(76°)

${\mathtt{h}} = {\frac{{\mathtt{609}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{76}}^\circ\right)}}} \Rightarrow {\mathtt{h}} = {\mathtt{627.643\: \!700\: \!274\: \!085\: \!654\: \!1}}$

so h = 627.64m to the nearest hundredth of a meter.

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