Question

Easy maths question please help

Answer 1

Answer:

12.649

Skills needed: Trigonometry

Step-by-step explanation:

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

Soh Cah Toa

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

Soh = Sine Opposite Hypotenuse

---> Cah = $cos(\angle x) = \frac{adjacent}{hypotenuse}$ ($cos(\angle x)$ 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 = $tan(\angle x) = \frac{opposite}{adjacent}$ ($tan(\angle x)$ 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:

$\tan \angle x = \frac{opposite}{adjacent}$

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

$\tan 31 = \frac{7.6}{\overline{BC}}$ --> 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 $\tan 31$

$\overline{BC} = \frac{7.6}{tan 31}$

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

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

$12.6485$ 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))