Question

Need to explain a bit on why the answer is 11.95. Show work

Answer 1

Step-by-step explanation:

Use the trigonometric ratio cosine.

Remember that
`\cos(x) = \frac{\textrm{adjacent}}{\textrm{hypotenuse}}`.

So, we can construct the following equation using the given triangle:

`\cos(23\textdegree)=(11)/(x)`

And solve for x. First, take the reciprocal of both sides (flip both sides).

`(\cos(23\textdegree))/(1)=(11)/(x)`

↓

`(1)/(\cos(23\textdegree))=(x)/(11)`

Then, multiply both sides by 11.

`11\cdot\left((1)/(\cos(23\textdegree))\right)=\left((x)/(11)\right) \cdot 11`

`(11)/(\cos(23 \textdegree)) = x`

`x = (11)/(\cos(23 \textdegree))`

Finally, plug this fraction into your calculator as 11/cos(23) to get approximately 11.95.

Also, make sure that your calculator's mode is degrees, NOT radians.