#Please help me!

38 messages · Page 1 of 1 (latest)

near moatBOT
still ginkgo
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ill try to help, one sec im working it out

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sorry im stumped too...

low stump
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Easy bro no problem so yeah, Let's call the right triangle ABC, where AB is the hypotenuse, AC is the leg with length 1, and BC is the leg with length 7. Let's call the point where the bisector of angle BAC intersects the side BC "D", and let's call the length of the shorter part of BC "x".

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ADB + ADC = 90

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so

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we have

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tan(theta) = AD/BD
tan(theta) = AD/CD

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AD/BD = AD/CD

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so simplified it's CD = BD

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Now we can use the fact that BD + CD = BC, and substitute CD with BD to get:
BD + BD = 7 - x
2BD = 7 - x

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tan(theta) = 1/BD
ADB + ADC = 90
2BD = 7 - x
tan(theta) = 1/BD
ADB = tan(theta) * BD
ADC = tan(theta) * (7 - x - BD)

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then substituting these expressions into the equation ADB + ADC = 90, we get:

tan(theta) * BD + tan(theta) * (7 - x - BD) = 90

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so we have 7 - x = BD / tan(theta)

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2 * (7 - x) / tan(theta) = 7 - x

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We simplify this equation and get 14 - 2x = 7tan(theta) - xtan(theta)

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so x = (14 - 7tan(theta)) / (2 - tan(theta))

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and to finish

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x = (14 - 7tan(26.56)) / (2 - tan(26.56)) ≈ 0.62

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So we finished: the length of the shorter part of BC is approximately 0.62.

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@jaunty kindle You understood ?

low stump
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ur welcome !

jaunty kindle
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The hypotenuse (AB) is the longest side of the triangle. The legs are CB and AC.

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CB = 7 > AC = 1. So this means that AB and CB are the longest sides of the triangle.

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@low stump

low stump
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|
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| /
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| / X
1 |/______\ 7
hypotenuse

jaunty kindle
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huh

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the hypotenuse is opposite of the 90 degrees

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angle

low stump
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|
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| /
| /
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1 | / \ 7
|/________
| AXB
|

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So AD/DB

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Equal to AC/CB

jaunty kindle
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but 7 is a leg

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not the hypotenuse

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i mean as long as OP got the question correct 💀

low stump
void rampart
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.solved OP never knew the length was 7(√50 - 7) ≈ 0.4975