3 years ago

If tan a = 1, find a.

Mathematics

1 answer:

Artist 52 [7]3 years ago

3 0

Answer:

a=45

Step-by-step explanation:

tan a= 1

tan a= tan45

a=45

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sweet-ann [11.9K]

Answer:

3. 3 : 5; 3: 5

Step-by-step explanation:

First, let's find the leght of the sides of each octagon.

$A= 18in^{2}$

The area of an octagon is defined by

$A=2(1+\sqrt{2})l^{2}$

Replacing the area

$18=2(1+\sqrt{2})l^{2}\\\frac{18}{2(1+\sqrt{2})} =l^{2}\\l=\sqrt{\frac{18}{3.4} } \approx 2.3 \ in$

Therefore, the side of the first octagon is 1.6 inches long.

Its perimeter is: $P=8(2.3in)=18.4in$

$A=50 in^{2}$

$50=2(1+\sqrt{2})l^{2}\\\frac{50}{2(1+\sqrt{2})} =l^{2}\\l=\sqrt{\frac{50}{3.4} } \approx 3.8 \ in$

Therefore, the side of the second octagon is 3.8 inches long.

Its perimeter is $P=8(3.8in)=30.4in$ .

Now, let's divide to find each ratio:

$\frac{3.8}{2.3} \approx 1.65$ (the ratio between sides).

$\frac{30.4}{18.4} \approx 1.65$ (the ratio between perimeters).

Therefore, the closest ratio is 3. 3 : 5; 3: 5

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3 years ago

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