Question

PLEASE HELP Rex, Paulo, and Ben are standing on the shore watching for dolphins. Paulo sees one surfacedirectly in front of him about a hundred feet away. Find the distances between Rex, Ben, Pauloand the dolphin. The angles between Rex, Ben, and the dolphin are marked on the diagram.Part I: Using triangle BCD, find the distance between Rex and the dolphin, and between Rexand Paulo. Assume the distance between Paulo and the dolphin is exactly 100 feet. Roundyour answers to one decimal place. Show your work. (4 points, 2 points each distance)Distance between rex and dolphin? Distance between rex and paulo ? distance between ben and paulo ?

Answer 1

You have that the distance between Paulo and the dolphin is 100ft, that is, the length of CD is 100ft.

To find the distance between Rex and the dolphin and Ben and the dolphin, you first use the greater triangle ABC, and also you take into account that the summ of the interoir angles of a triangle is 180°.

Then, for angle C you have:

∠C = 180 - 30 - 60 = 90°

Furthermore, for angle ∠BCD you have:

∠BCD = 180 - 90 - 30 = 60

and for angle ∠ACD:

∠ACD = 180 - 60 - 90 = 30

Now, consider that for a 30-60-90 triangle, the hypotenuse is twice the length of the shorter length. Thus, for the distance between the Ben and the dolphin BC you have a triangle with its shorter leg equal to 100ft.

Then, you have for the hypotenuse h:

h = BC = 2(100ft)

h = BCa = 200ft

Next, for the distance between Rex and the dolphin use the right triangle of the figure. Consider the greater leg is √3 time the shorter one.

Then, for greater leg (side CD) related to shorter leg (side AD) you have:

√3CD = AD replace the value of CD and solve for AD