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The top of a dam has an angle of elevation of 1.1 radians from a point on a river. Measuring the angle of elevation to the top of the dam from a point 155 feet farther downriver is 0.8 radians; assume the two angle measurements are taken at the same elevation above sea level. How high is the dam? (Round your answer to the nearest whole number.)

Respuesta :

Answer: 335ft

Step-by-step explanation:

The tangent of the angle of elevation is the ratio of the dam height h to the horizontal distance downriver of the observer. This gives us two equations for the height:

h= atan(1.1) = (155+a) tan(0.8)

⟹a= h/tan(1.3), 155+a= h/tan(0.8).

Subtracting the first equation from the second,

155=(155+a)−a =h/tan(0.8)−h/tan(1.1)

=h(1/tan(0.8)−1/tan(1.1)).

Solving for h,

h=155 ft (1tan(0.8)−1tan(1.1))−1

155(0.9713 - 0.5090)^-1

155(2.1631) ≈335 ft .

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