I need help finding bc and ac

Question

asked Feb 21, 2021 197k views

1 Answer

Zidar · Answer 1 · 2021-02-27T22:55:34+0000

From point A,

$\bf tan A = (perpendicular)/(base)$

$\bf \implies tan A = (BC)/(AB)$

$\bf \implies tan A = (BC)/(7)$

Now, we are given ∠A = 45°

$\bf \implies tan A = tan 45^(\circ)$

$\bf \implies tan 45^(\circ) = (BC)/(7)$

Now, we know that tan45° = 1

$\bf \implies 1 = (BC)/(7)$

$\bf \implies 1 * 7 = BC$

$\bf \implies BC = 7$

Now, by Pythagoras' theorem,

AC² = BC² + AB²

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

$\bf \implies AC^(2) = 49 + 49$

$\bf \implies AC^(2) = 98$

$\bf \implies AC = √(98)$

$\bf \implies AC = 7 √(2)$

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