Question

From the information given in the figure, point M A find the value of x and also sides AC and BC.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

∠BAC=90°,  ∠ABC=60°, ∠BCA=30°

$AC=5\sqrt{3}$ and $BC=10$

Step-by-step explanation:

Given the ΔABC, the three angles in terms if x which are 3x, 2x and x and also the side AB is 5 cm. we have to find all the angles and remaining two sides of the given triangle ABC.

By angle sum property of triangle,

∠BAC+∠ABC+∠BCA=180°

⇒ 3x+2x+x=180°

⇒ 6x=180° ⇒ x=30°

Hence, angles are ∠BAC=3x=3(30°)=90°

                               ∠ABC=2x=2(30°)=60°

                               ∠BCA=x=30°

Hence, BAC is right-angled triangle

$tan60^{\circ}=\frac{AC}{AB}=\frac{AC}{5}$

⇒ $\sqrt{3}\times 5=AC$

Hence, $AC=5\sqrt{3}cm$

$cos60^{\circ}=\frac{AB}{BC}=\frac{5}{BC}$

⇒ $\frac{1}{2}=\frac{5}{BC}$

Hence, $BC=10cm$