Education1st Corinthians annotated bAALEKS - Jameson Colley - Le XBest Al Homework HelperByteLearnhttps://Www-awu.aleks.com/alekscgi/×/Isl.exe/10_u-IgNsIkasNW8D8A9PVRDtYDggnR9...Import favoritesMVNU Students Ho...AALEKS - Jameson C...Trigonometric Identities and EquationsSolving a trigonometric equation modeling a real-world situationJamesonEspañolSuppose a projectile is fired from a cannon with velocity v0 and angle of elevation θ. The horizontal distance R(θ) it travels (in feet) is given by the following.R(θ)=32(v0)2sin2θIf v0=160ft/s, what angle θ (in radians) should be used to hit a target on the ground 492 feet in front of the cannon?Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a radian. (If there is more than one answer, enter additional answers with the
Q. Education1st Corinthians annotated bAALEKS - Jameson Colley - Le XBest Al Homework HelperByteLearnhttps://Www-awu.aleks.com/alekscgi/×/Isl.exe/10_u-IgNsIkasNW8D8A9PVRDtYDggnR9...Import favoritesMVNU Students Ho...AALEKS - Jameson C...Trigonometric Identities and EquationsSolving a trigonometric equation modeling a real-world situationJamesonEspañolSuppose a projectile is fired from a cannon with velocity v0 and angle of elevation θ. The horizontal distance R(θ) it travels (in feet) is given by the following.R(θ)=32(v0)2sin2θIf v0=160ft/s, what angle θ (in radians) should be used to hit a target on the ground 492 feet in front of the cannon?Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a radian. (If there is more than one answer, enter additional answers with the
Identify Given Values: Identify the given values and the formula to use.Given: v0=160ft/s, R(θ)=492feet, and the formula R(θ)=32(v0)2sin(2θ).
Substitute Known Values: Substitute the known values into the formula to solve for sin(2θ).R(θ)=((160)2⋅sin(2θ))/32=4928000⋅sin(2θ)=492sin(2θ)=492/8000sin(2θ)=0.0615
Solve for sin(2θ): Solve for 2θ using the inverse sine function.2θ=arcsin(0.0615)2θ≈0.062 radians
Solve for 2θ: Solve for θ by dividing 2θ by 2.θ=20.062θ≈0.031 radians
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