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
- Math - Write whether the statement is true or false. If false write a true ...
- Geometry - x ________________<20* |<90* y | |<70* (hypotenuse length ...
- Math - Yesterday I learned to solve a right triangle assuming I know the 3 ...
- 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 ...
- Math - Geometry - Two right triangles are touching at the tips. The left ...
- geometry - show that the sum of the squares of the lengths of the medians of ...