Question

Find the value of x and y rounded to the nearest tenth.

Answer 1

I hope this helps you

Answer 2

Answer:

(D)

Step-by-step explanation:

From the given figure, we have

AB=34 and AD=x and BD=y.

Since, ∠D=45° and ∠B=30°, therefore using the angle sum property, we have

∠A+∠B+∠D=180°

⇒∠A+45+30=180

⇒∠A=105°

Now, using the sine formula, we have

$\frac{x}{sin30^{\circ}}=\frac{34}{sin45^{\circ}}$

⇒$x=\frac{34{\times}sin30^{\circ}}{sin45^{\circ}}$

⇒$x=\frac{34\sqrt{2}}{2}$

⇒$x=24.0$

And, $\frac{y}{sin105^{\circ}}=\frac{34}{sin45^{\circ}}$

⇒ $y=\frac{34{\times}sin105^{\circ}}{sin45^{\circ}}$

⇒$y=\frac{34{\times}0.965}{0.707}$

⇒$y=46.4$

Therefore, the values of x and y are 24 and 46.4 respectively.

Thus, option D is correct.