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Trigonometric Identities and Equations
Solving a trigonometric equation modeling a real-world situation
Jameson
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Suppose a projectile is fired from a cannon with velocity 
v_(0) and angle of elevation 
theta. The horizontal distance 
R(theta) it travels (in feet) is given by the following.

R(theta)=((v_(0))^(2)sin 2theta)/(32)
If 
v_(0)=160ft//s, what angle 
theta (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 "or" button.)

theta=◻rad

◻ or
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Education\newline11st Corinthians annotated b b \newlineA\newlineALEKS - Jameson Colley - Le X X \newlineBest Al Homework Helper\newlineByteLearn\newlinehttps://Www-awu.aleks.com/alekscgi/×/Isl.exe/1010_u-IgNsIkasNW88D88A99PVRDtYDggnR99...\newlineImport favorites\newlineMVNU Students Ho...\newlineA\newlineALEKS - Jameson C...\newlineTrigonometric Identities and Equations\newlineSolving a trigonometric equation modeling a real-world situation\newlineJameson\newlineEspañol\newlineSuppose a projectile is fired from a cannon with velocity v0 v_{0} and angle of elevation θ \theta . The horizontal distance R(θ) R(\theta) it travels (in feet) is given by the following.\newlineR(θ)=(v0)2sin2θ32 R(\theta)=\frac{\left(v_{0}\right)^{2} \sin 2 \theta}{32} \newlineIf v0=160ft/s v_{0}=160 \mathrm{ft} / \mathrm{s} , what angle θ \theta (in radians) should be used to hit a target on the ground 492492 feet in front of the cannon?\newlineDo 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

Full solution

Q. Education\newline11st Corinthians annotated b b \newlineA\newlineALEKS - Jameson Colley - Le X X \newlineBest Al Homework Helper\newlineByteLearn\newlinehttps://Www-awu.aleks.com/alekscgi/×/Isl.exe/1010_u-IgNsIkasNW88D88A99PVRDtYDggnR99...\newlineImport favorites\newlineMVNU Students Ho...\newlineA\newlineALEKS - Jameson C...\newlineTrigonometric Identities and Equations\newlineSolving a trigonometric equation modeling a real-world situation\newlineJameson\newlineEspañol\newlineSuppose a projectile is fired from a cannon with velocity v0 v_{0} and angle of elevation θ \theta . The horizontal distance R(θ) R(\theta) it travels (in feet) is given by the following.\newlineR(θ)=(v0)2sin2θ32 R(\theta)=\frac{\left(v_{0}\right)^{2} \sin 2 \theta}{32} \newlineIf v0=160ft/s v_{0}=160 \mathrm{ft} / \mathrm{s} , what angle θ \theta (in radians) should be used to hit a target on the ground 492492 feet in front of the cannon?\newlineDo 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
  1. Identify Given Values: Identify the given values and the formula to use.\newlineGiven: v0=160ft/sv_{0} = 160 \, \text{ft/s}, R(θ)=492feetR(\theta) = 492 \, \text{feet}, and the formula R(θ)=(v0)2sin(2θ)32R(\theta) = \frac{(v_{0})^{2} \sin(2\theta)}{32}.
  2. Substitute Known Values: Substitute the known values into the formula to solve for sin(2θ)\sin(2\theta).R(θ)=((160)2sin(2θ))/32=492R(\theta) = \left((160)^2 \cdot \sin(2\theta)\right) / 32 = 4928000sin(2θ)=4928000 \cdot \sin(2\theta) = 492sin(2θ)=492/8000\sin(2\theta) = 492 / 8000sin(2θ)=0.0615\sin(2\theta) = 0.0615
  3. Solve for sin(2θ)\sin(2\theta): Solve for 2θ2\theta using the inverse sine function.\newline2θ=arcsin(0.0615)2\theta = \arcsin(0.0615)\newline2θ0.0622\theta \approx 0.062 radians
  4. Solve for 2θ2\theta: Solve for θ\theta by dividing 2θ2\theta by 22.\newlineθ=0.0622\theta = \frac{0.062}{2}\newlineθ0.031\theta \approx 0.031 radians

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