Question

What is the value of x

Answer 1

x = 3

Explanation:

using the sine ratio in right triangle ABC and the exact value

sin45° =
`(1)/(√(2) )` , then

sin45° =
`(opposite)/(hypotenuse)` =
`(BC)/(AC)` =
`(BC)/(6√(2) )` =
`(1)/(√(2) )` ( cross- multiply )

BC ×
`√(2)` = 6
`√(2)` ( divide both sides by
`√(2)` )

BC = 6

using the cosine ratio in right triangle BCD and the exact value

cos60° =
`(1)/(2)` , then

cos60° =
`(adjacent)/(hypotenuse)` =
`(BD)/(BC)` =
`(x)/(6)` =
`(1)/(2)` ( cross- multiply )

2x = 6 ( divide both sides by 2 )

x = 3

Answer 2

`\text{In}~ \triangle ABC,\\\\~~~~~~~~\sin 45^(\circ) =(BC)/(AC) \\\\\implies \frac 1{\sqrt 2} = (BC)/(6\sqrt 2)\\\\\\ \implies BC= 6\\\\\text{Now, In}~ \triangle BCD\\\\~~~~~~\cos 60^(\circ) = (BD)/(BC)\\\\\ \implies \frac 12 = (x)/(6)\\\\\\\implies x = \frac 62\\\\\\\implies x = 3`