Using the following triangle, what is the tangent of angle B?
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9514 1404 393
Answer:
195 ft
Step-by-step explanation:
The relationship between the horizontal distance, angle, and vertical height is given by ...
Tan = Opposite/Adjacent
Referring to the attached diagram, we have ...
tan(16°) = BT/MB
tan(25°) = BK/MB
Solving for BT and BK, we can describe their difference as ...
BT = MB·tan(16°)
BK = MB·tan(25°)
BK -BT = 35 = MB(tan(25°) -tan(16°))
Dividing by the coefficient of MB gives ...
MB = 35/(tan(25°) -tan(16°)) = 35/0.179562
MB = 195 . . . feet
Marcos is standing 195 feet from the base of the tree.
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I like to picture things though.
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Ok, by definition of "half," just multiply the number of rectangles by 2.
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2 x 2 = 4 after cutting it in half again.
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4 rectangles now!!
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Doing it the other way... pretend you are starting over from scratch.
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A new batch of brownies!
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But still pay attention to what you already cut.
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Cut down the middle the other direction.
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8.
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Now, finally, we multiply the half of the half brownies.
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What's 8 x 2?
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16.
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16 slices.
.
Maybe you didn't.
.
I like to picture things though.
.
Ok, a rectangle cut in half.
.
Ok, by definition of "half," just multiply the number of rectangles by 2.
.
1 x 2 = 2 after cutting the brownies in half.
.
2 x 2 = 4 after cutting it in half again.
.
4 rectangles now!!
.
Doing it the other way... pretend you are starting over from scratch.
.
A new batch of brownies!
.
But still pay attention to what you already cut.
.
Cut down the middle the other direction.
.
What's 4 x 2?
.
8.
.
Now, finally, we multiply the half of the half brownies.
.
What's 8 x 2?
.
16.
.
16 slices.