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story problem

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Two wires stretch from a pole to two points on the ground which are 25 feet apart. The first wire is to the left of the pole and forms a 30° angle with the ground. The second wire is to the right of the pole and forms a 60° angle with the ground. How tall is the pole? Simplify your answer.

I figured out how to draw it but do not understand how to solve

  • story problem -

    the wires form a 30-60-90 right triangle, with the ground as the hypotenuse

    both of the smaller triangles are similar to the large triangle

    the length of the 2nd wire is half of the distance between the wires

    use Pythagoras or trig to find the height of the pole

  • story problem -

    so would I do 25^2+135^2=x^2

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