Question

It’s number 11. find the value of x to the nearest tenth. please help thank you!

Answer 1

d

Explanation:

using the tangent ration in the left- side right triangle

tan56 =
`(opposite)/(adjacent)` =
`(115)/(y)` ( y represents the adjacent side )

multiply both sides by y

y × tan56° = 115 ( divide both sides by tan56° )

y =
`(115)/(tan56)` ≈ 77.6

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using the tangent ratio in the large outer right triangle

tan35° =
`(opposite)/(adjacent)` =
`(115)/(x+y)` ( multiply both sides by x + y )

(x + y) × tan35° = 115 ( divide both sides by tan35° )

x + y =
`(115)/(tan35)` ≈ 164.2

then

x + 77.6 = 164.2 ( subtract 77.6 from both sides )

x = 86.6

Answer 2

Explanation:

`tan \ 56 =(opposite \ side )/(adjacent \ side)\\\\\\1.4825=(115)/(y)\\\\y=(115)/(1.4825)\\\\\\`

y = 77.6

`tan \ 35 =(115)/(x+77.6)\\\\0.7*(x +77.6) =115\\\\x + 77.6 =(115)/(0.7)\\\\`

x + 77 .57 = 164.2

x = 164.2 - 77.6

x = 86.6