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Explanation as well please.

Explanation As Well Please class=

Sagot :

Answer:

[tex]\sf A\:\!F[/tex] = 77.3 cm

Step-by-step explanation:

[tex]\sf A\:\!F[/tex] is the diagonal of rectangle AEFB and divides it into two congruent right triangles, AEF and ABF. Therefore, [tex]\sf A\:\!F[/tex] is the hypotenuse of right triangle ABF. To find the length of [tex]\sf A\:\!F[/tex], we can use the Pythagorean Theorem. However, we first need to determine the length of BF.

BF is the hypotenuse of right triangle BCF, where BC = 60 cm and ∠FBC = 25°. Since BC is the side adjacent to angle FBC, and we need to find the hypotenuse BF, we can use the cosine trigonometric ratio:

[tex]\sf \cos FBC=\dfrac{BC}{BF} \\\\\\\cos 25^{\circ}=\dfrac{60}{BF} \\\\\\BF=\dfrac{60}{\cos 25^{\circ}}[/tex]

Now, use the Pythagorean Theorem to find the length of [tex]\sf A\:\!F[/tex]:

[tex]\sf A\:\!F^2=AB^2+BF^2 \\\\\\ A\:\!F^2=40^2+\left(\dfrac{60}{\cos 25^{\circ}}\right)^2 \\\\\\ A\:\!F=\sqrt{1600+\left(\dfrac{60}{\cos 25^{\circ}}\right)^2} \\\\\\ A\:\!F=77.3485241966... \\\\\\A\:\!F=77.3\; cm\;(3\;s.f.)[/tex]

So, the length of [tex]\sf A\:\!F[/tex] correct to 3 significant figures is:

[tex]\LARGE\boxed{\boxed{\sf 77.3\; cm}}[/tex]

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