Question

Choose the correct value of x AND the correct value of y from the choices below.

y
45°
16
x = 8/3
x = 8
y=8V2
y=8V3
y = 8
x = 82

Answer 1

x =
`(16)/(√(2) )` and y =
`(16)/(√(2) )`

Explanation:

Applying the trigonometric functions to the given triangle;

i. To determine the value of x;

Sin θ =
`(opposite)/(hypotenuse)`

Sin 45 =
`(x)/(16)`

x = 16 * Sin 45

= 16 *
`(1)/(√(2) )`

x =
`(16)/(√(2) )`

ii. To determine the value of y;

Cos θ =
`(adjacent)/(hypotenuse)`

Cos 45 =
`(y)/(16)`

y = 16 * Cos 45

= 16 *
`(1)/(√(2) )`

y =
`(16)/(√(2) )`

Thus, x =
`(16)/(√(2) )` and y =
`(16)/(√(2) )`