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
More Related Questions
- Math - Write whether the statement is true or false. If false write a true ...
- math plz check ;-; - A triangle has sides of lengths 5 cm, 5 cm, and square root...
- math plz check ;-; sorry - A triangle has sides of lengths 5 cm, 5 cm, and ...
- math - according to the triangle inequality, the length of the longest side of a...
- Math - True or false and if false write a true statement 1. A right triangle has...
- trig - In a certain right triangle, the two sides that are perpendicular to each...
- math plz help ;-; - A triangle has sides of lengths 5 cm, 5 cm, and square root ...
- MATH - can we sketch a triangle with 1:2:3 side-length ratio???? Intuitively, no...
- Math - Yesterday I learned to solve a right triangle assuming I know the 3 ...
- Geometry - x ________________<20* |<90* y | |<70* (hypotenuse length ...