Find the value of x to the nearest tenth . The image is below .

Question

asked Nov 3, 2024 93.7k views

1 Answer

Dhg · Answer 1 · 2024-11-10T06:44:53+0000

Answer :

Step-by-step explanation :

Let us consider two triangles,
$\sf\triangle ABC$ and
$\sf \triangle BDC,$

In
$\sf\triangle ABC$ ,

Using pythagoras theorm,

$\sf (H)^2= (B)^2 + (P)^2$

$\sf (AC)^2 = (BC)^2 + (AB)$

$\sf (9)^2 (BC)^2 +(8)^2$

$\sf 81 = (BC)^2 + 64$

$\sf (BC)^2 = 81-64$

$\sf (BC)^2= 17$

$\sf BC = \sqrt 17$

In
$\sf \triangle BDC,$

Using pythagoras theorm,

$\sf (H)^2= (B)^2 + (P)^2$

$\sf (BC)^2= (BD)^2 + (CD)^2$

$\sf (\sqrt 17 )^2 =(x)^2 + (3)^2$

$\sf 17 = x^2 + 9$

$\sf 17-9= x^2$

$\sf 8 = x^2$

$\sf x = \sqrt 8$

$\sf x = 2.8$