Question

I need the answers to 17 and 18 plz

Answer 1

Answer:

17. BC is 13 √ 2 or 18.38 units.

18. x = 7.

Step-by-step explanation:

1. Let's solve the question 17.

If AC = 26, find BC.

AC is the hypotenuse of the Δ ABC and let's recall that the sides of an square are equal, thus BC = AB = CD = AD

For finding BC , we will use Pythagorean theorem:

Hypotenuse ² = Side ₁ ² + Side₂ ²

Length of Side = x

26 ² = x ² + x ² (BC = AB in a square)

676 = 2x²

338 = x² (Dividing by 2)

x = √ 169 * 2

x = 13 √ 2

BC = 13 √ 2 = 18.38

BC is 13 √ 2 or 18.38 units.

2. Let's solve question 18.

If ∠ ACB = (11x - 32) °, find the value of x.

Recall that a square has four right angles (90 °), thus:

∠ BCD = 90°

But in this case, we're asked to find ∠ ACB , that  is formed by the line AC that intersects C in two equal angles : ∠ ACB and ∠ ACD, thus:

∠ ACB and ∠ ACD = 45°

Then, let's find the value of x:

11x - 32 = 45

11x = 45 + 32 (Adding 32 to both sides)

11x = 77

x = 77/11 (Dividing by 11 at both sides)

x = 7