Question

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

x = 38 , y = 19

Explanation:

using the tangent ratio in the right triangle and the exact valu

tan30° =
`(1)/(√(3) )` , then

tan30° =
`(opposite)/(adjacent)` =
`(y)/(19√(3) )` =
`(1)/(√(3) )` ( cross- multiply )

`√(3)` × y = 19
`√(3)` ( divide both sides by
`√(3)` )

y = 19

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using the cosine ratio in the right triangle and the exact value

cos30° =
`(√(3) )/(2)` , then

cos30° =
`(adjacent)/(hypotenuse)` =
`(19√(3) )/(x)` =
`(√(3) )/(2)` ( cross- multiply )

`√(3)` × x = 38
`√(3)` ( divide both sides by
`√(3)` )

x = 38