Question

Please help me out with this

Answer 1

x = 6.5 cm

Explanation:

The tangent to the circle forms a right angle with the radius x

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides

The hypotenuse is (x + 14.7) ← opposite the right angle, hence

(x + 14.7)² = x² + 20.2² ← expand parenthesis on left side

x² + 29.4x + 216.09 = x² + 408.04 ( subtract x² from both sides )

29.4x + 216.09 = 408.04 ( subtract 216.09 from both sides )

29.4x = 191.95 ( divide both sides by 29.4 )

x ≈ 6.5 cm

Answer 2

Explanation:

Formula

a^2 + b^2 = c^2

Givens

a = x

b = 20.2

c = 14.7 + x

Solution

x^2 + 20.2^2 = (14.7 + x)^2 Expand the brackets

x^2 + 408.04 = 14.7^2 + 29.4x + x^2 Cancel the x^2

408.04 = 216.9 + 29.4x Subtract 216.9 from both sides.

191.98 = 29.4x Divide by 29.4

6.52993 = x Answer.

6.5 to the nearest tenth.