Hailey is scuba diving in the ocean. her boat is anchored 300 feet away at a 30° angle of depression. if her diving partner is 25 feet directly below her, how far is hailey's diving partner from the boat? (round to nearest whole number)

Distance between partner and boat is 360 feet.

Step-by-step explanation:

Hailey is scuba diving in the ocean. If she is at point O then angle of depression is 30°.

Distance AB is 300 feet and her diving partner is 25 feet below her at point C.

We have to calculate the measurement of BC which is the distance of Hailey's partner from the boat.

From ΔAOB

tan 30 = AO/300

AO = 300×tan30 = 300×(1/√3) = 100√3 feet = 173.21 feet

From ΔABC

By Pythagoras theorem

BC² = AB² + AC² = AB² + (173.21+25)²

BC² = 300²+(198.21)² = 90000 + 39287.2 = 129287.2

BC = √129287.2 = 359.57 = 360 feet

So the distance is 360 feet.

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step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.