Trapeze - a geometrical figure with four corners which two parties are parallel each other and are called the bases, and two others - are not parallel and are called side.
Instruction
1. Let's consider two tasks with different initial data. Task 1. Find side of an isosceles trapeze if BC basis = b, AD basis = d and a corner is known at BAD side = the Alpha. Decision: Lower a perpendicular (trapeze height) from B top before crossing with the big basis, receive BE piece. Write down AB on a formula through corner size: AB = AE/cos(BAD) = AE/cos (Alpha).
2. Find AE. It will be equal to the difference of lengths of two bases divided in half. So: AE = (AD are BC)/2 = (d - b)/2. Now find AB = (d - b) / (2*cos (Alpha)). CDs = are equal to AB in an isosceles trapeze of length of sides, therefore, = (d - b) / (2*cos (Alpha)).
3. Task 2. Find AB trapeze side if b knows the top basis of BC =; lower basis of AD = d; BE height = h and a corner at opposite side of CDA is equal the Alpha. Decision: Carry out the second height from top of C before crossing with the lower basis, receive CF piece. Consider a rectangular triangle of CDF, find the party of FD on the following formula: FD = CD*cos(CDA). Find length of side of CD from other formula: CD = CF/sin(CDA). So: FD = CF*cos(CDA)/sin(CDA). CF = BE = h, therefore, FD = h*cos (Alpha)/sin (Alpha) = h*ctg (Alpha).
4. Consider a rectangular triangle of ABE. Knowing lengths of its parties of AE and BE, you can find the third party - AB hypotenuse. Length of the party of BE, AE is known to you find as follows: AE = AD - BC - FD = d - b - h*ctg (Alpha). Using the following property of a rectangular triangle - the square of a hypotenuse is equal to the sum of squares of legs - find AB: AB(2) = h(2) + (d - b - h*ctg (Alpha)) (2). Value of side of a trapeze of AB to equally square root from the expression located in the right side of equality.