Question

Construct a angle ABC such that AB =2.5cm, BC =6cm, and AC =6.5vm. measure Angle B =? . can you verify Pythagoras theorem for this triangle.

Answer 1

If we have ABC is a ∆

AC > BC and AB

AC( Hypotenuse ) =6.5 cm

BC( Base ) = 6 cm

AB( Height ) = 2.5 cm

AC²=AB²+BC²

6.5²=2.5²+6²

42.25=6.25+36

42.25= 42.25

LHS = RHS

It satisfy Pythagoras theorem .


Hence prove

The given ∆ is also Right angle

Answer 2

$\textbf {Hey there, here is the solution.}$

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AB = 2.5cm (Given)

BC = 6cm (Given)

AC = 6.5 cm (Given)

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We use cosine rule , a² = b² + c² - 2bc cos A, to find the angle B.

6.5² = 2.5² + 6² - 2(2.5) (6) cos∠B

42.45 = 6.25 + 36 - 30 cos ∠B

42.45 = 42.45 - 30 cos ∠B

30 cos∠B = 0

cos ∠B = 0

∠B= 90°

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We will use Pythagoras; Theorem, a² + b² = c², to prove that this is a right triangle.

AC being the longest length = hypotenuse

.

a² + b² = c²

c² = 2.5² + 6²

c² = 42.45

c = √42.45

c = 6.5

Since we get 6.5 cm for C ⇒ it is a right triangle.

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$\textbf {I hope it helps.}$