Question

in a right triangle x y z , x z is the hypotenuse of length 12 cm and angle x is equal to 45 degree the area of the triangle is
A. 72cm^2
B. 12cm2
C. 24cm2
D. 36cm2

Answer 1

Answer:-

Option D

Step-by-step-explaination:-

To find the other two sides :-

$\mathsf{ \sin45 = \frac{opp}{hyp} = \frac{yz}{xz}}$

$\mathsf{ \frac{1}{ \sqrt{2} } = \frac{yz}{xz}}$

$\mathsf{ \frac{12}{ \sqrt{2}} \times \frac{ \sqrt{2} }{ \sqrt{2}} = yz }$

$\mathsf{yz = 6 \sqrt{2}}$

$\mathsf{ \cos45 = \frac{xy}{xz}}$

$\mathsf{ \frac{1}{ \sqrt{2} } = \frac{xy}{12}}$

$\mathsf{xy = 6 \sqrt{2}}$

$\mathsf{area \: of \: triangle = \frac{1}{2} bh }$

$\mathsf{ = \frac{1}{2} \times 6 \sqrt{2} \times 6 \sqrt{2} }$

$\mathsf{ = 18 \times 2}$

$\mathsf{ = 36 {cm}^{2} }$

Answer 2

36CM2

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