Question

Find A and B. Using the image above.

Answer 1

a = 7, b =
`(7√(3) )/(3)`

Explanation:

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

sin45° =
`(1)/(√(2) )` , then

sin45° =
`(opposite)/(hypotenuse)` =
`(a)/(7√(2) )` =
`(1)/(√(2) )` ( cross- multiply )

a ×
`√(2)` = 7
`√(2)` ( divide both sides by
`√(2)` )

a = 7

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

tan60° =
`√(3)` , then

tan60° =
`(opposite)/(adjacent)` =
`(a)/(b)` =
`(7)/(b)` =
`√(3)` ( multiply both sides by b )

b ×
`√(3)` = 7 ( divide both sides by
`√(3)` )

b =
`(7)/(√(3) )` ×
`(√(3) )/(√(3) )` =
`(7√(3) )/(3)`