An vulture is perched 40 ft up in a tree and looks down at an angle of depression of a 35? angle and spots roadkill. How far is the roadkill from the vulture? Round to the nearest tenth

The function sine of angle of 35 degrees is equal to divide the opposite side to the angle of 35 degrees (the height of the vulture in a tree) by the hypotenuse ( the distance from the vulture to the roadkill)

Let

z -----> the distance from the vulture to the roadkill

sin(35°)=40/z

z=40/sin(35°)=69.7 ft

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ApusApus ApusApus · Answer 2 · 2019-08-17T04:23:28+02:00

Answer:

69.7 feet.

Step-by-step explanation:

Let x represent the distance between vulture and roadkill.

We have been given that a vulture is perched 40 ft up in a tree and looks down at an angle of depression of a 35 and spots roadkill.

We can see from the attachment that vulture, roadkill and angle of depression forms a right triangle with respect to ground, where, x is hypotenuse and 40 ft is opposite side.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(35^{\circ})=\frac{40}{x}[/tex]

[tex]x=\frac{40}{\text{sin}(35^{\circ})}[/tex]

[tex]x=\frac{40}{0.573576436351}[/tex]

[tex]x=69.7378718[/tex]

[tex]x\approx 69.7[/tex]

Therefore, the roadkill is 69.7 feet away from the vulture.