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What is the height of a building when the distance between its angles of elevation which are 29 degrees and 37 degrees is 30 meters on level ground?
Using trigonometry its height works out as 63 meters to the nearest meter. -------------------------------------------------------------------------------------------------------- let: h = height building α, β be the angles of elevation (29° and 37° in some order) d be the distance between the elevations (30 m). x = distance from building where the elevation of angle α is measured. Then: angle α is an exterior angle to the triangle which contains the position from which angle α is measured, the position from which angle β is measured and the point of the top of the building. Thus angle α = angle β + angle at top of building of this triangle → angle α > angle β as the angle at the top of the building is > 0 → α = 37°, β = 29° Using the tangent trigonometric ratio we can form two equations, one with angle α, one with angle β: tan α = h/x → x = h/tan α tan β = h/(x + d) → x = h/tan β - d → h/tan α = h/tan β - d → h/tan β - 1/tan α = d → h(1/tan β - 1/tan α) = d → h(tan α - tan β)/(tan α tan β) = d → h = (d tan α tan β)/(tan α - tan β) We can now substitute the values of α, β and x in and find the height: h = (30 m × tan 37° × tan 29°)/(tan 37° - tan 29°) ≈ 63 m
What is 6 plus plus 6 plus 63 plus 63 plus 36 plus?
6 plus 6 plus 63 plus 63 plus 36 plus 36 is equal to 210.
What is 50 plus 63 plus 72 plus 63 plus 137 plus 172?
50 + 63 + 72 + 63 + 137 + 172 = 557
What is 24 plus 63?
24 + 63 = 87
What is 1000 plus 56 plus 63?
1000 + 56 + 63 = 1,119
