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.)

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 .

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.