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Construct a $△ ABC$ with $AB = 3 cm, BC = 4 cm$ and $AC = 5 cm$ and find a measure of $m ∠ ABC$

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30^{\circ}

53^{\circ}

43^{\circ}

90^{\circ}

answer is D.

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Detailed Solution

We have a

△ ABC

with sides AB of 3 cm, BC of 4 cm and AC of 5 cm and we need to determine the
measure of angle

∠ ABC

Here, let us try to observe the relation among the lengths of sides of

△ ABC

. We have

AB = 3 cm, BC = 4 cm, AC = 5 cm

Let us calculate the value of

A B^{2} + B C^{2}

from the given triangle. Hence, we get

A B^{2} + B C^{2} = (3)^{2} + (4)^{2} = 9 + 14

A B^{2} + B C^{2} = 25

…………(i)
And hence, we can observe that the value of

(AC)^{2}

can be given 25 as length AC is of 5 cm. So, we get

(AC)^{2} = 25

………………(ii)
Now, we know the Pythagoras theorem for a right angle triangle is defined by the relation Question Image

(hypotenuse)^{2} = (perpendicular)^{2} + (base)^{2}

…………………. (iv)
Where the opposite angle of hypotenuse is

90^{\circ}

Hence, on comparing the relations (iii) and (iv), we get that (AC) is acting as a hypotenuse for the

△ ABC

Hence the measure of the angle B should be

90^{\circ}

to follow the Pythagoras rule.
Hence, we get

m ∠ ABC = 90^{\circ}

Correct option is 4.

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