Question

Help me solve,Brainlist for first to answer

Answer 1

Answer:

(i) the other two sides are 6 and  6$\sqrt{2}$

(ii) the other two sides are   $\frac{4}{3} and \frac{8}{3}$

Step-by-step explanation:

(i)  Sine: sin(θ) = Opposite ÷ Hypotenuse

    Cosine: cos(θ) = Adjacent  ÷ Hypotenuse

    Tangent: tan(θ) = Opposite ÷ Adjacent

Here adjacent side = 6

opposite side = d

angle = 45°

other angles are 90° and 45°

tan (45) = Opposite ÷ Adjacent

 1 = d ÷ 6

∴ d = 6 × 1 = 6

so opposite side = 6

Hypotenuse ² = opposite side ² + adjacent side²

                      =  6² + 6²

                      = 36 + 36

                       = 72

hypotenuse = $\sqrt{72}$

                     = 6$\sqrt{2}$

the other two sides are 6 and  6$\sqrt{2}$

(ii) here adjacent side = 4√3

angle = 30°

other angles are 90° and 60°

opposite side = d

tan ( 30) = opposite ÷ adjacent

 $\frac{1}{\sqrt{3}}$ = d ÷ 4√3

$\frac{1}{\sqrt{3}}$ = d × ($\frac{\sqrt{3}}{4}$)

                       3 d = 4

therefore d = $\frac{4}{3}$

therefore opposite side = $\frac{4}{3}$

Hypotenuse ² = opposite side ² + adjacent side²

                        =( $\frac{4}{3}$)² +( $\frac{4}{\sqrt{3}}$)²

                        = $\frac{64}{9}$

therefore hypotenuse = $\sqrt{\frac{64}{9}}$

                                     =$\frac{8}{3}$

the other two sides are   $\frac{4}{3} and \frac{8}{3}$