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

Answer:

C

Step-by-step 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 = $\sqrt{8}$ = 2$\sqrt{2}$

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Using the sine ratio in Δ ABD with the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , then

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{AB}{DB}$ = $\frac{2\sqrt{2} }{DB}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

$\sqrt{3}$ × DB = 4$\sqrt{2}$ ( divide both sides by $\sqrt{3}$ )

DB = $\frac{4\sqrt{2} }{\sqrt{3} }$ ( multiply numerator/ denominator by $\sqrt{3}$ to rationalise denominator )

     = $\frac{4\sqrt{2} }{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$

     = $\frac{4\sqrt{6} }{3}$ → C