# Trignometry

posted by Stranger

ABCD is a square where M and N are midpoints of AD and CD, respectively. If sin∠MBN=a/b, where a and b are coprime positive integers, what is the value of a+b?

1. Steve

If we let x = ∠MBN and y=∠ABM=∠NBC, then
x+2y = pi/2
sin x = sin(pi/2-2y) = cos 2y = 1-2sin^2 y
Now, siny = 1/√5, so
sinx = 1 - 2(1/5) = 3/5
a+b=8

## Similar Questions

1. ### Math

Let S(n) denote the sum of digits of the integer n. Over all positive integers, the minimum and maximum values of S(n)/S(5n) are X and Y, respectively. The value of X+Y can be written as a/b , where a and b are coprime positive integers. …
2. ### geometry

ABCD is a square of side length 1. E , F , G and H are the midpoints of AB , BC , CD and DA , respectively. The lines FA , AG , GB , BH , HC , CE , ED and DF determine a convex 8-gon. By symmetry, this octagon has equal sides. If s …
3. ### vmps

ABCD is a square where M and N are midpoints of AD and CD , respectively. If sinÚMBN=a b , where a and b are coprime positive integers, what is the value of a+b ?
4. ### Trignometry

The angles in triangle ABC satisfy 6sin∠A=3√(3)sin∠B=2√(2)sin∠C. If sin^2∠A=a/b, where a and b are coprime positive integers, what is the value of a+b?
5. ### geometry

The angles in triangle ABC satisfy 6sin∠A=3√3sin∠B=2√2sin∠C. If sin2∠A=a/b, where a and b are coprime positive integers, what is the value of a+b?
6. ### maths

The angles in triangle ABC satisfy 6sin∠A=3√3sin∠B=2√2sin∠C. If sin^2∠A=ab, where a and b are coprime positive integers, what is the value of a+b?
7. ### Trigonometry question?

Let ABCD be a square, and let M and N be the midpoints of BC and CD respectively. Find sin<MAN.
8. ### geometry...TRIANGLE

ABCD is a quadrilateral with ∠ADC=∠ACD, ∠ACB=∠ABC and CD=7. If triangles ADC and ABC have perimeter 51 and 59, respectively, what is the value of BC?
9. ### helllllppp math

In a tetrahedron ABCD, the lengths of AB, AC, and BD are 6, 10, and 14 respectively. The distance between the midpoints M of AB and N of CD is 4. The line AB is perpendicular to AC, BD, and MN. The volume of ABCD can be written as …
10. ### heeeeeelp math

In a tetrahedron ABCD, the lengths of AB, AC, and BD are 6, 10, and 14 respectively. The distance between the midpoints M of AB and N of CD is 4. The line AB is perpendicular to AC, BD, and MN. The volume of ABCD can be written as …

More Similar Questions