Question

Solve for x. Leave your answer in simplest radical form.

Answer 1

There are two Right angled triangles in the given figure, with two missing sides, let's name the other missing side be " y "

According to Pythagoras theorem,

$\boxed{ \large \boxed{h {}^{2} = {b}^{2} + p{}^{2} }}$

note :

• p = perpendicular / opposite side
• b = base / adjacent side
• h = hypotenuse

let's solve for " y² " first ( square of other missing side )

$➢ \: \: {y}^{2} = {8}^{2} + 3 {}^{2}$

$➢ \: \: {y}^{2} = 64 + 9$

$➢ \: \: {y}^{2} = 73$

now let's solve for " x " , by using pythagorous theorem

$➢ \: \: {x}^{2} = {y}^{2} + {6}^{2}$

$➢ \: \: {x}^{2} = 73 + 36$

$➢ \: \:x {}^{2} = 109$

$➢ \: \: x = \sqrt{109}$

Approximate :

$➢ \: \: 10.44 \: \: units$

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