Trigonometry, question.  Jim stood at the bottom of a hill and measured an angle of evelation of 40 degrees to the top of the hill. He also measured the length a path of the hill to be 15m. What is the verticle distance from the top of the ill to the ground?

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We can draw a right-angled triangle where the length from Jim to the top of the hill is the hypotenuse of the right-angled triangle.  The angle at the base of the hill is 40 degrees.  The question is asking about the vertical distance from the top of the hill to the ground, which is the vertical leg of the triangle.

To find this height, let's call it x.  Then the height is the opposite side of the angle given.  We also know the hypotenuse.  This means that we use the sine ratio

`sin 40=O / H`   where O is the opposite and H is the hypotenuse.

`sin40=x/15`   now solve for x by multiplying by 15

`15sin40=x`

`x=9.64`

The vertical distance of hill to ground is 9.64m.

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