The picture below shows a box sliding down a ramp: a right triangle abc has measure of angle abc equal to 90 degrees and measure of angle acb equal to 68 degrees. the length of ab is 14 feet. what is the distance, in feet, that the box has to travel to move from point a to point c?

the box has to travel 15. feet   to move from point a to point c.

explanation

for finding the distance of traveling to move from point a to point c, we need to find the length of side ac in the triangle.

according to the diagram, in right angle triangle abc,   side ab is the opposite and side ac is the hypotenuse in respect of ∠acb.

given that, ∠acb = 68° and   ab = 14 feet

as,

so, in triangle

sin(∠acb) =

[tex]sin(68)= \frac{14}{ac}\\ \\ ac= \frac{14}{sin(68)}\\ \\ ac= 15./tex]

so, the box has to travel 15. feet   to move from point a to point c.

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step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.