Question

Which is closest to the value of x

Answer 1

11

Explanation:

Here we are given a right angled triangle with a known angle of 41°, length of the hypotenuse to be 14 and we are to find the length of the base x.

For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.

`cos \alpha =(base)/(hypotenuse)`

So putting in the given values to get:

`cos 41=(x)/(14) \\\\x= cos 41*14\\\\x=10.56`

Therefore, the value of x is the closest to 11.

Answer 2

11

Explanation:

The mnemonic SOH CAH TOA reminds you that

... Cos = Adjacent/Hypotenuse

so you know ...

... cos(41°) = x / 14

Multiplying by 14 gives the value of x.

... x = 14·cos(41°) ≈ 10.566 ≈ 11

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Comment on answer choices

The visible answers are 10, 40, 12. The best choice of those is 10. If there is no choice offering 11 as the answer, then I'd choose 10.