Question

Which of the following is true about the right triangle?

cos(a)= 3/5
sin(a)= 3/5
sin(a)= 4/5
tan(a)= 3/4
tan (a)= 4/3

Answer 1

Option 1.
`cos (a) = (3)/(5)`, option 3.
`sin (a) = (4)/(5)`, and option 5.
`tan (a) = (4)/(3)` are true about the right triangle.

Explanation:

Step 1:

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Here the hypotenuse measures 15 units. Assume the other side measures x.

`15^(2) = x^(2) +9^(2) , x^(2) = 15^(2) -9^(2) .`

`x^(2) = 144, x= 12.`

Step 2:

`sin \theta = (oppositeside)/(hypotenuse) ,cos \theta = (adjacentside)/(hypotenuse) , tan \theta = (oppositeside)/(adjacentside).`

For angle A, the opposite side is 12 units long, the adjacent side is 9 units long and the hypotenuse is 15 units long.

`sin (a) = (12)/(15) ,cos(a) = (9)/(15) , tan(a) = (12)/(9).`

`sin (a) = (4)/(5) ,cos (a) = (3)/(5) , tan (a) = (4)/(3).`

So option 1.
`cos (a) = (3)/(5)`, option 3.
`sin (a) = (4)/(5)`, and option 5.
`tan (a) = (4)/(3)` are true about the right triangle.