# trig

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.

1. 👍 0
2. 👎 0
3. 👁 39
1. 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 √ ??

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### math/geometry

complete the statements: To find the length of the hypotenuse of a 45-45-90 triangle, multiply the length of one of the legs by:? Could the answer be .5??? to find the length of the shorter leg of a 30-60-90 triangle, multiply the

asked by Lauren on December 5, 2009
2. ### math

I have 14 questions and I was wondering if someone could check my answers. This is a do or die situation. If I don't get an A, I may not get to graduate. I really appreciate you taking your time to double check theses for me.

asked by Brittany on April 2, 2011
3. ### Math

Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the largest triangle is 8 centimeters. What is the number of centimeters in the length of the

asked by Jerry on December 29, 2015
4. ### geometry

Theres a right triangle. its hypotenuse is 30. There is a line in the triangle making a smaller one. this breaks the hypotenuse to 24 and 6. I need to find the length of the other sides If i can figure out how to post a picture i

5. ### MATH MS.SUE HELP PLEASE!

Could somebody help me I don't understand any of this. Could someone show me or tell me how to work the problems? 1. Find the length of the hypotenuse of a right triangle with the legs of 9cm and 12cm A.8 B.21 C.15 D.225 2.The

asked by bob on October 18, 2013
6. ### Algebra

Hi. 1. I have a right triangle here. I know that I am to use the Pythagorean Theorem: a^2 + b^2 = c^2. In this case, side a is (x + 4) and b is x. The hypotenuse is 4 + (x + 4) So here we have the equation: (x + 4)^2 + x^2 = 4 +

asked by Student on March 11, 2014
7. ### corollary to isosceles triangle theorem

how to prove 1)the measure of each angle of an equilateral triangle is 60. 2)the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Thanks. 1) The angles in any triangle have to add up

asked by Jen on November 17, 2006
8. ### n2maths

the length of the hypotenuse of a rigth triangled triangle is 10cm more than the length of the longer of the 2sides. calculate the lengths of the hypotenuse and the other unknow n side if the length of the shortest side is 50 cm

asked by alistar on September 17, 2014
9. ### Math Algebra

The length of the hypotenuse of a right triangle is 30 m. The length of one leg is 20 cm. Find the length of the other leg. Round your answer to the nearest tenth I know how to do hypotenuse but this doesn't seem to work

asked by Deborah on December 16, 2012
10. ### math

5. Find the length of the hypotenuse of a right triangle with legs of 20 cm and 21 cm. 41 cm 841 cm 6 cm 29 cm 6. The length of the hypotenuse of a right triangle is 15 cm. The length of one leg is 9 cm. Find the length of the

asked by hi, help hard questions on November 29, 2012

More Similar Questions