A ship is at a distance of 200 m from a tall tower. What is the angle of depression (to the nearest degree) of the ship found by a man after climbing 50 m up the tower?

14degrees

Step-by-step explanation:

Given the following

Distance of ship from the tower = 200m

Height of the tower = 50m

Required

Angle of depression theta

USing the SOH CAH TOA identity

Tan theta = opposite/adj

Tan theta = 50/200

Tan theta = 1/4

theta = arctan(0.25)

theta = 14.03degrees

Hence the angle of depression is 14degrees

answer: the answer is 40.82

step-by-step explanation: 3.14 x 13(or half of 26) to the power of 2

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.