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December 18, 2014

December 18, 2014

Posted by **dat** on Sunday, May 8, 2011 at 11:56am.

all three angles of the triangle equals 2. What are the lengths of the other two sides

of the triangle?

(A) 5 and 5p3

(B) 5p2 and 5p2

(C) 1 and3

p11 (D) 4 and 2p21

(E) None of the above.

- trig -
**Reiny**, Sunday, May 8, 2011 at 2:15pmlet the other two sides be a and b

then a^2 + b^2 = 100

the cotangents of the two acute angles are

a/b + b/a and of course the cot 90° = 0

a/b + b/a + 0 = 2

then a^2 + b^2/ab = 2

a^2 + b^2 = 2ab

a^2 - 2ab + b^2 = 0

(a - b)^2 = 0

a-b = 0

a = b

sub back into a^2 + b^2 = 100

a^2 + a^2 = 100 , since a=b

a^2 = 50

a = 5√2

also if a^2 = 50

then b^2 = 50 and b= 5√2

It must be an isosceles right-angled triangle with the other sides 5√2 each

check: tan (of angle) = (5√2/5√2) = 1

so 1 + 1 + 0 = 2

Is (5√2)^2 + (5√2)^2 = 100 ? yes!

is your "p" supposed to say √ ??

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