Question

If Dave is standing next to a silo of cross-sectional radius

r = 9

feet at the indicated position, his vision will be partially obstructed. Find the portion of the y-axis that Dave cannot see. (Hint: Let a be the x-coordinate of the point where line of sight #1 is tangent to the silo; compute the slope of the line using two points (the tangent point and (12, 0)). On the other hand, compute the slope of line of sight #1 by noting it is perpendicular to a radial line through the tangency point. Set these two calculations of the slope equal and solve for a. Enter your answer using interval notation. Round your answer to three decimal places.)

Answer 1

Solution-

Let the circle with a center 'O' ( Origin) having radius = 9 .A point P at (12,0) .A line which is tangent to the circle at point Q that crosses through the point P(12,0).A point on the y axis be R where the tangent line is crosses the y axis.

The triangle ΔOQP formed is a right triangle with the right angle at Q .So,

We have OQ = 9 , OP= 12.So,

QP=√63

Now in triangle ΔRPO , the side OR is the length of the upper half of the y axis that the person is not able to see who is standing on point P(12,0).

Since ΔRPO is also a right triangle with the right angle at O. ∆OQP & ∆RPO triangles have an angle at P in common.So these two triangles are similar and their sides are proportional.

<POQ=<ORP

and OQ/RO = QP/OP

Putting the values of OQ=9, QP=√63 Aand OP=12

9/RO = √63/12

or 9×12=RO×√63

or ROx√63 = 9x12

or RO = 108/√63= 13.61

13.61 is the hidden part above the x axis.

So, The total hidden length =2× 13.61=27.22

Hence, the required answer is 27.22