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A hawk sees two mice on the ground in front of it, but $20\text{ft}$ apart. The angle of depression to mouse A is $25$ degrees and the angle of depression to mouse B is $35$ degrees. What is the horizontal distance from mouse A to the hawk? $\newline$

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Experimental probability

Full solution

Q. A hawk sees two mice on the ground in front of it, but

20\text{ft}

apart. The angle of depression to mouse A is

25

degrees and the angle of depression to mouse B is

35

degrees. What is the horizontal distance from mouse A to the hawk?

\newline

Denote horizontal distance: Let's denote the horizontal distance from mouse A to the hawk as $d$ . Since the hawk is looking down at mouse A with an angle of depression of $25$ degrees, we can use trigonometry to find $d$ . The angle of depression from the hawk to the ground is equal to the angle of elevation from the ground to the hawk. Therefore, we can use the tangent of the angle of elevation, which is also $25$ degrees, to find the horizontal distance $d$ . The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the hawk above the ground, which we'll call $h$ , and the adjacent side is the horizontal distance $d$ we're trying to find. So, we have: $\newline$ $\tan(25^\circ) = \frac{h}{d}$ $\newline$ We need to solve for $d$ , which means we need to know the height $h$ of the hawk above the ground. However, the height is not given in the problem, so we cannot calculate the horizontal distance $d$ without it.

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