Adjacent side over the hypotenuse.
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In mathematics, "tan" refers to the tangent function, which calculates the ratio of the opposite side to the adjacent side in a right triangle for a given angle. On the other hand, "tan⁻¹" (or arctan) is the inverse tangent function, which takes a ratio and returns the angle whose tangent is that ratio. Essentially, while tan gives you the tangent of an angle, tan⁻¹ helps you find the angle when you know the tangent value.
tan-1(0.4877) = 25.99849161 or about 26 degrees
For sinX you set it equal to the opposite side of the angle over the hypotenuse(SOH),cross multiply. CosX you set it equal to the adjacent side of the angle over the hypotenuse (CAH), cross multiply. Lastly for TanX set it equal to the opposite of the angle over the adjacent side of the angle and then cross multiply (TOA). I hope that's helpful :)
**Sin**e(angle) = opposite / hupotenuse NB **Cos**ine(angle) = adjacent / hypotenuse **Tan**gent(angle) = opposite/adjacent.
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