Question

CAN U EXPLAIN HOW TO SOLVE THIS?!

Answer 1

Find a right angle and multiply each side and then add them :) hope this helps

Answer 2

C

Explanation:

Use Δ ABC to find AB then Δ ABD to find DB

Δ ABC is isosceles since ∠ CAB = ∠ CBA = 45° , then CB = CA = 2

Using Pythagoras' identity in Δ ABC , then

AB² = 2² + 2² = 4 + 4 = 8 ( take square root of both sides )

AB =
`√(8)` = 2
`√(2)`

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Using the sine ratio in Δ ABD with the exact value

sin60° =
`(√(3) )/(2)` , then

sin60° =
`(opposite)/(hypotenuse)` =
`(AB)/(DB)` =
`(2√(2) )/(DB)` =
`(√(3) )/(2)` ( cross- multiply )

`√(3)` × DB = 4
`√(2)` ( divide both sides by
`√(3)` )

DB =
`(4√(2) )/(√(3) )` ( multiply numerator/ denominator by
`√(3)` to rationalise denominator )

=
`(4√(2) )/(√(3) )` ×
`(√(3) )/(√(3) )`

=
`(4√(6) )/(3)` → C