(GEOMETRY) Nancy dives to a point T under the sea. A surface buoy is anchored at point P. Points S, R, and Q are at different distances from T as shown in the figure below. Segment ST is parallel to segment RQ.

Which equation can be used to find the correct value of the distance d, in feet, between the buoy and Nancy?

Question

(GEOMETRY) Nancy dives to a point T under the sea. A surface buoy is anchored at point P. Points S, R, and Q are at different distances from T as shown in the figure below. Segment ST is parallel to segment RQ.



Which equation can be used to find the correct value of the distance d, in feet, between the buoy and Nancy?

anonymous · Answer

attachment

hartnn · Answer

do u realize that triangle PST and PRQ are similar?

anonymous · Answer

Yeah PRQ looks like it's just an extension @hartnn

hartnn · Answer

or should i prove it?

hartnn · Answer

there should atleast be 2 pairs of angles congruent in those 2 triangles:
angle P is common,so P=P
angle STP=RQP=90 given
so now they are similar triangles,proven mathematically,not just by looks :P .....

anonymous · Answer

@hartnn  Oh ok :) I see it

hartnn · Answer

so as i already told u that the ratio of corresponding sides are equal,
can u use this fact to solve further?

anonymous · Answer

@hartnn Yeah I understood it on the other problem, for some reason I feel like it's the first answer choice, but the numbers are making me a little fuzzy.

anonymous · Answer

$$d=55 \text{*Tan}\left[\text{ArcTan}\left[\frac{25}{85-55}\right]\right]=55 $$

mertsj · Answer

The third one.