If a triangle has angles 45- 45- and 90- what is the value of B C when A C-28 -2 m-A- 32 mB- 17 mC- 28 mD- 13 m

The correct option is C 28 mWe have theorem : " If the angles of a triangle are 45^∘, 45^∘, and 90^∘,then each of the perpendicular sides is 1/√(2) times the ...

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Standard IX

Mathematics

45-45-90 Degrees Triangle Theorem

If a triangle...

Question

If a triangle has angles $45^{\circ}, 45^{\circ}$ , and $90^{\circ}$ , what is the value of BC when AC = $28 \sqrt{2}$ m .

13 m

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32 m

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17 m

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28 m

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Solution

The correct option is D 28 m
We have theorem :

" If the angles of a triangle are $45^{\circ}, 45^{\circ}$ , and $90^{\circ}$ ,then each of the perpendicular sides is $\frac{1}{\sqrt{2}}$ times the hypotenuse " .

AC= hypotenuse = $28 \sqrt{2}$ m .

So, BC = $\frac{1}{\sqrt{2}} \times 28 \sqrt{2} = 28 m$

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If a triangle has angles 45∘,45∘, and 90∘, what is the value of BC when AC = 28√2 m .

The correct option is D 28 mWe have theorem : " If the angles of a triangle are 45∘,45∘, and 90∘,then each of the perpendicular sides is 1√2 times the hypotenuse " . AC= hypotenuse = 28√2 m . So, BC = 1√2×28√2=28 m

If a triangle has angles $45^{\circ}, 45^{\circ}$ , and $90^{\circ}$ , what is the value of BC when AC = $28 \sqrt{2}$ m .