Question

What is the hypotenuse?

18
9√2
√18
18√2

Answer 1

BC = 18

Explanation:

Since ∠B = ∠C then the triangle is isosceles and so

∠B = ∠C = 45°

Using the sine ratio in the right triangle and

sin45° =
`(1)/(√(2) )`, then

sin45° =
`(opposite)/(hypotenuse)` =
`(AC)/(BC)` =
`(9√(2) )/(BC)`

Multiply both sides by BC

BC × sin45° = 9
`√(2)`, that is

BC ×
`(1)/(√(2) )` = 9
`√(2)`

Multiply both sides by
`√(2)`

BC = 9
`√(2)` ×
`√(2)` = 9 × 2 = 18