In order to estimate the height of a building, two students stand at a certain distance from the building at street level. from this point, they find the angle of elevation from the street to the top of the building to be 39°. they then move 300 feet closer to the building and find the angle of elevation to be 50°. assuming that the street is level, estimate the height of the building to the nearest foot.

758 ft

Step-by-step explanation:

Note: Refer to the figure

Now from the figure:

In Δ AOD

tan 39° = H/(300 + x)      .................(1)

and in Δ BOD

tan50° = H/x   .................(2)

on dividing 1 by 2 we get

0.6794 = x/(300 + x)

or

203.84 + 0.6794x = x

or

0.3206x = 203.84

or

x = 635.80 ft

now using the equation (2)

we get

tan 50° = H/x

or

H = xtan50°

on substituting the value of x, we get

H = 635.80 × tan 50

or

H = 757.72 ft ≈ 758 ft

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

details

step-by-step explanation: