Question

I need help finding bc and ac

Answer 1

Given :

• AB = 7
• ∠A = 45°

To Find :

• BC = ?
• AC = ?

Solution :

From point A,

$\bf tan A = \dfrac{perpendicular}{base}$

$\bf \implies tan A = \dfrac{BC}{AB}$

$\bf \implies tan A = \dfrac{BC}{7}$

Now, we are given ∠A = 45°

$\bf \implies tan A = tan 45^{\circ}$

$\bf \implies tan 45^{\circ} = \dfrac{BC}{7}$

Now, we know that tan45° = 1

$\bf \implies 1 = \dfrac{BC}{7}$

$\bf \implies 1 \times 7 = BC$

$\bf \implies BC = 7$

Now, by Pythagoras' theorem,

AC² = BC² + AB²

$\bf \implies AC^{2} = (7)^{2} + (7)^{2}$

$\bf \implies AC^{2} = 49 + 49$

$\bf \implies AC^{2} = 98$

$\bf \implies AC = \sqrt{98}$

$\bf \implies AC = 7 \sqrt{2}$

$\pink{\bf \therefore \: values \: of \: AC = 7 \sqrt{2} \: and \: BC = 7}$