Question

In a triangle ABC. the sides are AB 16 cm. AC 63 cm. BC 65 em. From A, a straight line AM is drawn up to the
midpoint M of side BC. Then the length of AM is equal to:
32.5 cm
24.5 cm
23.5 cm
31.5 cm

Answer 1

Answer:

the length of AM is equal to 24.5 cm

Answer 2

The length of AM is 32.5 cm.

Step-by-step explanation:

It is clear that Δ ABC is a right triangle.

As 65² = 63² + 16² and it satisfies the Pythagoras Theorem.

Now, see the diagram attached.

Here, $\tan y = \frac{16}{63}$

⇒ $y = \tan^{- 1}(\frac{16}{63}) = 14.25^{\circ}$

Now, considering the Δ AMC, using the property of the triangle, we have

$\cos 14.25^{\circ} = \frac{32.5^{2} + 63^{2} - x^{2}}{2 \times 32.5 \times 63}$

⇒ x² = 1056.249

⇒ x = 32.49 ≈ 32.5 cm.

Therefore, the length of AM is 32.5 cm. (Answer)