A surveyor measures the angle of elevation to a point on a mountain, that is 6 miles away, to be 15 degrees. The vertical change in the elevation from the point where the surveyor is standing to the point on the mountain is ??? miles. (Round your answer to the nearest hundredth of a mile)

Question

A surveyor measures the angle of elevation to a point on a mountain, that is 6 miles away, to be 15 degrees. The vertical change in the elevation from the point where the surveyor is standing to the point on the mountain is   ???     miles. (Round your answer to the nearest hundredth of a mile)

johnweldon1993 · Answer

I believe it would be like

|dw:1370377536803:dw|

since it asks for the vertical change

so what trig function uses an angle....a side adjacent to that angle...and a side opposite that angle?

anonymous · Answer

tangent

anonymous · Answer

i think

johnweldon1993 · Answer

Yes you are correct...tangent = opposite / adjacent

johnweldon1993 · Answer

so then how would you set up your equation?

anonymous · Answer

$$\tan 15 = \frac{ x }{ 6 }$$

johnweldon1993 · Answer

perfect...and then solve for 'x'

anonymous · Answer

but when i do it, it is less than six

johnweldon1993 · Answer

Don't forget...6 miles...is how far away he is seeing the mountain from....so from that distance...the vertical change between the mountain peak and his standing spot would be completely unrelated to the 6 miles away that he is

anonymous · Answer

oh, wow. Thanks man

johnweldon1993 · Answer

so the 1.61 miles that you should be getting...WOULD be the answer

anonymous · Answer

it makes sense now. ty

johnweldon1993 · Answer

no problem!