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 √ ??

## Answer This Question

## Related Questions

- Math - Write whether the statement is true or false. If false write a true ...
- Geometry - x ________________<20* |<90* y | |<70* (hypotenuse length ...
- math - according to the triangle inequality, the length of the longest side of a...
- Math - Yesterday I learned to solve a right triangle assuming I know the 3 ...
- trig - In a certain right triangle, the two sides that are perpendicular to each...
- C programming - Pythagorean Triples. A right triangle can have sides that are ...
- Math - True or false and if false write a true statement 1. A right triangle has...
- maths - shapes - Can you name these quadrilaterals? a) All sides are the same ...
- MATH - can we sketch a triangle with 1:2:3 side-length ratio???? Intuitively, no...
- geometry - Given the hypotenuse of a right triangle is 600, and the length of ...

More Related Questions