Engineers and surveyors often determine distances that cannot be measured directly by using similar triangles like the ones shown below.

using the information from the drawing, which of these is closest to the distance from point a on one bank to point e on the opposite bank?

a.59 feet
b.102 feet
c.118 feet
d.139 feet

102 ft.

Step-by-step explanation:

See the diagram attached.

From right triangle Δ ADC,  

⇒ AC = 160 ft. {Since }

Now, given that BC = 42 ft.

Hence, AB = AC - BC = 160 - 42 = 118 ft.

Now, from right triangle Δ AEB we can write

⇒ ft ≈ 102 ft.

Therefore, the closest distance from point A on one bank to point E on the opposite bank is 102 ft. (Answer)

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step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form