The base of a trapezoid are 397.62 and 254.15 respectively, the angles that the sides make with the longer base are 68°39.2' and 72°6.0'. Find the sides and the diagonal.
Need help with this pls.
since the height h is the same on both ends, and the extra length of the long base is 143.47, then
h = x tan 68°39.2' = (143.47-x) tan 72°6.0'
solve for x.
Now, one diagonal d is seen to be
d^2 = (x+254.15)^2 + h^2
and the side s nearest that vertex is
s^2 = h^2+x^2 (or s=x sec 68°39.2')
Now repeat at the other end.
To find the sides and the diagonal of a trapezoid given the bases and angles, we can apply the Law of Cosines, which states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides and the cosine of the included angle.
Let's denote the longer base as side a, the shorter base as side b, the first side (adjacent to the longer base) as side c, and the second side (adjacent to the shorter base) as side d.
1. Find the lengths of side c and side d:
To find the lengths of side c and side d, we will use the Law of Cosines.
c² = a² + b² - 2ab * cos(C)
d² = b² + a² - 2ab * cos(D)
Using the given values:
a = 397.62
b = 254.15
C = 68°39.2' = 68 + (39.2/60) ≈ 68.6533°
D = 72°6.0' = 72 + (6.0/60) ≈ 72.1000°
c² = 397.62² + 254.15² - 2*397.62*254.15 * cos(68.6533°)
d² = 254.15² + 397.62² - 2*254.15*397.62 * cos(72.1000°)
Calculate c and d by taking the square root of c² and d².
2. Find the diagonal of the trapezoid:
To find the diagonal of the trapezoid, we can use the Pythagorean theorem.
Diagonal² = c² + d²
Calculate the diagonal by taking the square root of (c² + d²).
By following these steps, you should be able to find the sides and diagonal of the trapezoid.