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3241004551 [841]
3 years ago
15

Lily is standing at horizontal ground level with the base of the Sears Tower. The angle formed by the ground and the line segmen

t from her position to the top of the building is 15.7°. The Sears Tower is 1450 feet tall. Find Lily's distance from the Sears Tower to the nearest foot.
Mathematics
1 answer:
Inessa05 [86]3 years ago
8 0
This is the concept of trigonometry, the distance of Lily from the tower will be given by:
tan theta=[opposite]/[adjacent]
opposite=1450 ft
adjacent=x ft
theta=15.7
thus;
1450/x=tan15.7
hence;
x=1450/tan15.7
x=5,158.54 ft
x=5,159 (to the nearest foot)
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The slope intercept form for a line is y = mx + b.
                                                                 ↑      <span>↑

m is the slope of the line or how steep it is. b is where the line runs into the y axis at one point. x and y are the values you plug in when you have a specific point you want to use (x, y).

For the first picture, you can see that the line "intercepts" or collides with the y axis at 1. Thus we know the b value.

To find the slope, you just pick 2 points on the line and plug them into a little equation (try to memorize this equation, it helps to find slope):

m = (y</span>₂ - y₁)/(x₂ - x₁)

The two points we'll use are (1, 0) and (0, 1) since x goes through both of
those points.                          ↑  ↑           ↑  ↑
                                              x₁ y₁        x₂ y<span>₂

m = (1 - 0)/(0 - 1)

m = 1 / -1

m = -1

This makes sense - since the slope is going downward, the slope is negative.

So the equation is:

y = -x + 1

____________________________________________________________

For the second problem, We  can see the line intercepts the y-axis at -5. That is our b value.

The the slope of this line is 0 since it is not going up or down, so that is our m value:

y = 0(x) - 5 = -5

The equation of the line is y = -5</span>
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