Alifeguard at position l spots a swimmer in trouble at one corner of the pool, s. she runs down the length of the pool to position p, and then dives in and swims a distance d from p and s.

show that the swimming distance is given by the relation d=wsecx
if l=2w, determine the range of values that x may take on, given that p can be anywhere along the length of the pool.

Let us assume the angle which the lifeguard makes at the point S be x°.

Now, we know that in a triangle,

i.e.

i.e. .

i.e. .

Hence, the distance is given by i.e. .

Further, we have that,

i.e.

i.e. ( As l=2w )

i.e.

i.e.

i.e.

So, the lifeguard can go from the path PS to MS i.e. the range of x is 1.107° to 90°

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.