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

In a right triangle the hypotenuse has length 10 and the the sum of the cotangents of

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 2:15pm
let 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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