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Illusion [34]
2 years ago
7

Find A and B. Using the image above.

Mathematics
1 answer:
NeX [460]2 years ago
7 0

Answer:

a = 7, b = \frac{7\sqrt{3} }{3}

Step-by-step explanation:

Using the sine ratio in the left right triangle and the exact value

sin45° = \frac{1}{\sqrt{2} } , then

sin45° = \frac{opposite}{hypotenuse} = \frac{a}{7\sqrt{2} } = \frac{1}{\sqrt{2} } ( cross- multiply )

a × \sqrt{2} = 7\sqrt{2} ( divide both sides by \sqrt{2} )

a = 7

--------------------------------------------------------

Using the tangent ratio in the right triangle on the right and the exact value

tan60° = \sqrt{3} , then

tan60° = \frac{opposite}{adjacent} = \frac{a}{b} = \frac{7}{b} = \sqrt{3} ( multiply both sides by b )

b × \sqrt{3} = 7 ( divide both sides by \sqrt{3} )

b = \frac{7}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } = \frac{7\sqrt{3} }{3}

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