In (triangle ) abc, ab = x, bc = y, and ca = 2x. a similarity transformation with a scale factor of 0.5 maps (triangle) abc to (triangle) mno, such that vertices m, n, and o correspond to a, b, and c, respectively. if om = 5, what is ab?

If a similarity transformation with a scale factor of 0.5 maps ΔABC to ΔMNO, such that vertices M, N, and O correspond to A, B, and C, respectively, then

Given AB = x, BC = y, and CA = 2x, you can write

Since OM = 5, you can find x: OM=x=5. Then AB=x=5.

AB=5.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: