Question

Please help me with this question regarding TRIGONOMETRY!

Answer 1

`\boxed{134.8 \: \mathrm{ft}}`

Explanation:

Let’s take triangle ACD.

Find length CD.

tan θ =
`(opposite)/(adjacent)`

tan (48) =
`(CD)/(110)`

110 tan (48) = CD

CD ≈ 122.167

Let’s take triangle BCD.

Find length BC.

sin θ =
`(opposite)/(hypotenuse)`

sin (65) =
`(122.167)/(BC)`

BC =
`(122.167)/(sin(65))`

BC ≈ 134.796

Answer 2

The answer is option 2.

Explanation:

First, you have to find the length of CD using Tangent Rule, tanθ = opposite/adjacent:

`\tan(θ) = (oppo.)/(adj.)`

`let \: θ = 48`

`let \: oppo. = cd`

`let \: adj. = ad = 110`

`\tan(48) = (cd)/(110)`

`cd = 110 \tan(48)`

`cd = 122.17 \: feet`

Next, you have to find the length of BC using Sine Rule:

`\sin(θ) = (oppo.)/(hypo.)`

`let \: θ = 65`

`let \: oppo. = cd = 122.17`

`let \: hypo. = bc`

`\sin(65) = (122.17)/(bc)`

`bc = (122.17)/( \sin(65) )`

`bc = 134.8 \: feet \: (near.tenth)`