How do I determine the length of the shorter base of a trapezoid from the longer base length, height, and...
How do I determine the length of the shorter base of a trapezoid from the longer base length, height, and only two angles?
An example would be 24" longer base, with 45 deg angles at both ends with only 1" in height. Both upper angles would be 135 deg.
What would the length of the shorter base be?
How do you solve for it?
Thanks!
geometry trigonometry
asked Jan 19 '17 at 6:08
Flexibull
11
add a comment |
How do I determine the length of the shorter base of a trapezoid from the longer base length, height, and only two angles?
An example would be 24" longer base, with 45 deg angles at both ends with only 1" in height. Both upper angles would be 135 deg.
What would the length of the shorter base be?
How do you solve for it?
Thanks!
geometry trigonometry
asked Jan 19 '17 at 6:08
Flexibull
11
add a comment |
How do I determine the length of the shorter base of a trapezoid from the longer base length, height, and only two angles?
An example would be 24" longer base, with 45 deg angles at both ends with only 1" in height. Both upper angles would be 135 deg.
What would the length of the shorter base be?
How do you solve for it?
Thanks!
geometry trigonometry
asked Jan 19 '17 at 6:08
Flexibull
11
How do I determine the length of the shorter base of a trapezoid from the longer base length, height, and only two angles?
An example would be 24" longer base, with 45 deg angles at both ends with only 1" in height. Both upper angles would be 135 deg.
What would the length of the shorter base be?
How do you solve for it?
Thanks!
geometry trigonometry
geometry trigonometry
asked Jan 19 '17 at 6:08
Flexibull
11
asked Jan 19 '17 at 6:08
Flexibull
11
asked Jan 19 '17 at 6:08
Flexibull
11
asked Jan 19 '17 at 6:08
Flexibull
11
asked Jan 19 '17 at 6:08
Flexibull
11
11
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
Suppose the longer base length is $b$ and the $2$ angles are $alpha$ and $beta$ with height being $h$
The shorter base length is
$$b-hcot alpha-hcot beta = b-h(cot alpha+ cot beta)$$
To see this, notice that the height and the base form perpendicular angle.
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
add a comment |
If you decompose the figure into a rectangle and two right triangles, and note the triangles are isosceles, you'll see the length you seek is a longer base minus the height doubled.
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
add a comment |
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2 Answers
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2 Answers
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Suppose the longer base length is $b$ and the $2$ angles are $alpha$ and $beta$ with height being $h$
The shorter base length is
$$b-hcot alpha-hcot beta = b-h(cot alpha+ cot beta)$$
To see this, notice that the height and the base form perpendicular angle.
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
add a comment |
Suppose the longer base length is $b$ and the $2$ angles are $alpha$ and $beta$ with height being $h$
The shorter base length is
$$b-hcot alpha-hcot beta = b-h(cot alpha+ cot beta)$$
To see this, notice that the height and the base form perpendicular angle.
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
add a comment |
Suppose the longer base length is $b$ and the $2$ angles are $alpha$ and $beta$ with height being $h$
The shorter base length is
$$b-hcot alpha-hcot beta = b-h(cot alpha+ cot beta)$$
To see this, notice that the height and the base form perpendicular angle.
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
Suppose the longer base length is $b$ and the $2$ angles are $alpha$ and $beta$ with height being $h$
The shorter base length is
$$b-hcot alpha-hcot beta = b-h(cot alpha+ cot beta)$$
To see this, notice that the height and the base form perpendicular angle.
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
answered Jan 19 '17 at 6:16
Siong Thye Goh
99.1k1464117
99.1k1464117
add a comment |
add a comment |
If you decompose the figure into a rectangle and two right triangles, and note the triangles are isosceles, you'll see the length you seek is a longer base minus the height doubled.
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
add a comment |
If you decompose the figure into a rectangle and two right triangles, and note the triangles are isosceles, you'll see the length you seek is a longer base minus the height doubled.
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
add a comment |
If you decompose the figure into a rectangle and two right triangles, and note the triangles are isosceles, you'll see the length you seek is a longer base minus the height doubled.
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
If you decompose the figure into a rectangle and two right triangles, and note the triangles are isosceles, you'll see the length you seek is a longer base minus the height doubled.
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
edited Feb 6 '17 at 15:28
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
answered Jan 19 '17 at 6:13
CiaPan
9,94311146
9,94311146
add a comment |
add a comment |
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