An airplane is flying at an altitude of 6 miles (approximately 32,000 feet) toward a point directly above where you are standing. If you are standing x miles away from a spot that is perpendicular to the plane, what is the equation that relates the angle as a function of x? Then, using that equation, solve for when x is 2 miles.

angle = arc tangent(6/x)

for x=2 -> angle = 71.565°

Step-by-step explanation:

To find the relation of the distance x and the angle of elevation that you are seeing the airplane, we should use the tangent relation of the angle. The opposite side of the angle is the altitude of the airplane, and the adjacent side of the angle is the distance x.

So we have that:

tangent(angle) = 6/x

angle = arc tangent(6/x)

If we have the value of x = 2, the angle will be:

angle = arc tangent(6/2) = arc tangent(3)

angle = 71.565°

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq