Atourist looks out from the observation deck of the space needle in seattle. the deck is at a height of 520 ft. she sees her friend on the ground below at an angle of depression of 80.2 what is the distance between the two? round your answer to the nearest tenth of a foot.

Last option 527.7 ft

Step-by-step explanation:

From the diagram attached we can see the angle of depression is 80.2 which is equal to ∠ACB (alternate angles)

Height of the deck AB = 520 ft. and we have to calculate the distance H between the tourist and her friend.

Sin ∠ACB =

Now we apply sin rule sin 80.2 =

So the tourist and her friend are 527.7 ft apart.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.