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There is no simple answer.
tan A, where the angle is measured in radians, is the sum of the infinite series whose nth term is
{(-1)^n*2^(2n+2)*[2^(2n+2)-1]*B(2n+2)/(2n+2)!}*A^(2n+1)
where B is a Bernoulli number.
Alternatively, a simpler definition is
sin(A) = A - A^3/3! + A^5/5! - A^7/7! + ...
cos(A) = 1 - A^2/2! + A^4/4! - A^6/6! + ...
and then tan(A) = sin(A)/cos(A).
Again, A must be in radians.
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What is the approximate height of a building when the angle of elevation at the top of a building is 34 degrees and at a point 80 feet closer the angle of elevation is 45 degrees?
It can be shown that:height = (d tan α tan β)/(tan α - tan β)where: α is the angle closest to the objectβ is the angle further away from the objectd is the distance from the point of angle α to the point of angle βThus: height = (80 ft × tan 45° × tan 34°)/(tan 45° - tan 34°) ≈ 165.78 ft
What is the height of a building if the angle of elevation to the top from a point on the ground is 31.4 degrees and from 53 feet further back it is 26.4 degrees?
It can be shown that:height = (d tan α tan β)/(tan α - tan β)where: α is the angle closest to the objectβ is the angle further away from the objectd is the distance from the point of angle α to the point of angle βThus: height = (53 ft × tan 31.4° × tan 26.4°)/(tan 31.4° - tan 26.4°) ≈ 140.87 ft
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 are the basic trigonometric ratios?
Sine(Sin) Cosine(Cos) Tangent(Tan) ---- -Sin of angle A=opposite leg of angle A / hypotenuse -Cos of angle A= Adjacent leg of angle A / Hypotenuse -Tan of angle A= opposite leg of angle A / Adjacent lef of angle A
What is the half angle exact value for Tan 165?
tan 165/2 = 1.068691
