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

Answer 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.

Answer 2

man 1.9m tall observes the angle of elevation of the top and bottom of a mast as 65° and 41° respectively.If the mast is mounted on a house 12m tall,find correct to 3 significant figures
I.distance of the man from the house
ii.length of the mast