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olga55 [171]
3 years ago
7

Help geometry bisecting angles

Mathematics
1 answer:
dusya [7]3 years ago
4 0

Since the angles are bisecting < RSU = < UST

substitution----- 4x+16=9x-9

subtract 4x from both sides----- 16=5x-9

add 9 to both sides-----25=5x

divide by 5 on both sides------ 5=x

The value of x is 5

substitute the value of x in both expressions

1st expression: 4x+16

substitute the value of x------ 4(5)+16= 20+16=36

2nd expression: 9x-9

substitute the value of x-----9(5)-9=45-9=36

< RST= <RSU+<UST

<RSU=36 degrees

<UST= 36 degrees

------------------------------------you have calculated both above-------------------------------------------

m<RST= 36 + 36=72 degrees


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9514 1404 393

Answer:

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Step-by-step explanation:

The left-side ratio of (2+4)/4 = 3/2 suggests BC is 3/2 times the length DE. If that were the case, BC = (3/2)(11) = 16.5, as Crow says.

The right-side ratio of (5+9)/9 = 14/9 suggests that BC 9 is 14/9 times the length DE. If that were the case, BC = (14/9)(11) = 154/9 = 17 1/9 ≈ 17.1, as Toad says.

The different ratios of the two sides (3/2 vs 14/9) tell you that the triangles are NOT similar, so the length of BC cannot be found by referring to the ratios of the given sides.

Rather, the Law of Cosines must be invoked, first to find angle A (109.471°), then to use that angle to compute the length of BC given the side lengths AB and AC. That computation gives BC ≈ 16.971. (See the second attachment.)

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