a man 1.9 metres to observe the angles of elevation of the top and bottom of your mouth as 65° and 41 degrees respectively if the mast is mounted on a house 12m high find to the three significant figures a) the distance of the Man from the house and b) the length of the mast

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  1. Draw a diagram. You can see that if the mast (not your mouth!) has height h, and the distance to the house is x, then
    (h+12-1.9)/x = tan65°
    (12-1.9)/x = tan41°
    eliminate x, and you have
    (h+12-1.9) cot65° = (12-1.9)cot41°
    Solve for h, and use that to find x.

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