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Trigonometry
Yes, sine, cosine, tangent definitions are based on right triangles
To find the tangent of 1, you can use the inverse tangent function (arctan) on a calculator. Simply input 1 into the arctan function and calculate the result. The tangent of 1 is approximately 0.7854.
If the pole is on level ground then you have the outline of a right angled triangle with an opposite side of 3 feet and an adjacent angle of 30 degrees. To find the length of the adjacent side (which in effect is the shadow of the pole) use the tangent ratio: tangent = opposite/adjacent which can be rearranged to: adjacent = opposite/tangent adjacent = 3/tangent 30o = 5.196152423 feet Therefore the shadow cast by the pole is 5.2 feet corrected to one decimal place.
you solve secant angles when you have the hypotenuse and adjacent sides. sec=1/cos or, cos^-1 (reciprocal identity property) Tangent is solved when you have adjacent and opposite sides, or you can look at it as its what you use when you dont have the hypotenuse. tan=sin/cos or tan=opp/adj or tan=y/x