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A tiny but horrible alien is standing at the top of the empire state building (which is 443 meters tall) and threatening to destroy the city of new york! a men in black agent is standing at ground level, 18 meters across the street, aiming his laser gun at the alien. at what angle, in degrees, should the agent shoot his laser gun? round your final answer to the nearest tenth

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JeanaShupp

Answer: [tex]87.7^{\circ}[/tex]


Step-by-step explanation:

Height of the building AB= 443 meters

Distance between the building and the agent at the ground BC= 18 meters

Let x be the angle the agent should shoot his laser gun

Since ΔABC is a right triangle, then

[tex]\tan\ x=\frac{AB}{BC}[/tex]

[tex]\Rightarrow\tan\ x=\frac{443}{18}\\\Rightarrow\tan\ x=24.6111\\\Rightarrow\ x=\tan^{-1}(24.61)\\\Rightarrow\ x=87.67^{\circ}\approx87.7^{\circ}[/tex]




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The agent needs to shoot at an angle of 87.67°

To solve this question, we would use trigonometric ratio SOHCAHTOA;

Data;

  • opposite = 443m
  • adjacent = 18
  • θ =?

Tangent of the Angle

Since we have the value of opposite and adjacent, we can easily use tangent of an angle to find the angle in which the agent needs to shoot.

[tex]Tan\theta = \frac{opposite}{adjacent}\\ Tan \theta = \frac{443}{18}\\ tan \theta = 24.61\\\theta= tan^-^1(24.61)\\\theta = 87.67^0[/tex]

From the calculations above, the agent needs to shoot at an angle of 87.67°

Learn more on angle of elevation here;

https://brainly.com/question/2881595

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