Two watch towers at aa historic fort are located 375m apart. The first tower is 14m tall, and the second tower is 30 m tall.
a)What is the angle of depression from the top of the second tower to the top of the first tower?
b)The guards in the towers simultaneously spot a suspicious car parked between the towers. The angle of depression from the lower tower to the car is 7.7 degrees. The angle of depression from the highest tower is 6.3 degrees. Which guard is closer to the car? Explain how you know?
Just looking for how about I would go solving a question like this in preperation for my next test, thanks!
+130490 a) The angle of depression is given by ..
tanΘ = 16/375 ....using the tangent inverse, we have
tan-1(16/375) = about 2.4°
b) The distance - d - the car is from the lower tower is given by
tan(7.7) = 14/d rearrange
d = 14/ tan(7.7) = about 103.54 m
Then.....the car must be closer to this tower since the towers are 375 m apart
Just as a check....the distance -d - that the car is from the higher tower is given by :
tan(6.3) = 30/d rearrange
d = 30/tan(6.3) = 271.73 m ...the car is more distant from this tower...!!!
+130490 a) The angle of depression is given by ..
tanΘ = 16/375 ....using the tangent inverse, we have
tan-1(16/375) = about 2.4°
b) The distance - d - the car is from the lower tower is given by
tan(7.7) = 14/d rearrange
d = 14/ tan(7.7) = about 103.54 m
Then.....the car must be closer to this tower since the towers are 375 m apart
Just as a check....the distance -d - that the car is from the higher tower is given by :
tan(6.3) = 30/d rearrange
d = 30/tan(6.3) = 271.73 m ...the car is more distant from this tower...!!!
