Question

Easy maths question please help

Answer 1

12.649

Skills needed: Trigonometry

Explanation:

1) We need to use one of the fundamentals of trigonometry, which is:

Soh Cah Toa

---> Soh =
`sin(\angle x) = (opposite)/(hypotenuse)` (
`sin(\angle x)` equals the side Opposite of it divided by the Hypotenuse -- sin is short for sine (pronounced as sign)

Soh = Sine Opposite Hypotenuse

---> Cah =
`cos(\angle x) = (adjacent)/(hypotenuse)` (
`cos(\angle x)` equals the side adjacent (not the hypotenuse) to the angle divided by the hypotenuse -- cos is short for cosine (pronounced as co-sign)

Cah = Cosine Adjacent Hypotenuse

---> Tan =
`tan(\angle x) = (opposite)/(adjacent)` (
`tan(\angle x)` equals the side opposite of it divided by the side (not hypotenuse) adjacent to it -- tan is short for tangent

Tan = Tangent Opposite Adjacent

2) In this case, we are solving for adjacent:

This is because
`\overline{BC}` is next to
`\angle \theta` and
`\overline{BC}` is not the hypotenuse (
`\overline{AC}` is the hypotenuse as it is opposite the right angle)

---> We are given opposite as side
`x` is opposite
`\angle \theta`

3) Let's plug it in:

`\tan \angle x = (opposite)/(adjacent)`

`\angle \theta = 31, adjacent = 7.6, opposite = \overline{BC}`

`\tan 31 = \frac{7.6}{\overline{BC}}` --> Here, we should multiply both sides by
`\overline{BC}`

`\overline{BC} * \tan 31 = 7.6` --> To get
`\overline{BC}` by itself, divide both sides by
`\tan 31`

`\overline{BC} = (7.6)/(tan 31)`

You have to plug this into the calculator as you cannot mentally solve trig functions.

---> Plugging it into calc:
`\overline{BC} = (7.6)/(\tan 31) = 12.6485 \text{ rounded to the ten-thousandths place}`

`12.6485` is rounded to the ten-thousandths, but the problem asks for 3 SF, so that would be
`12.649` (rounded that 85 to 9 (or 90))