Question

What would you use to solve for a?

a
43
11
A
A. sine
B. cosine
C. tangent D. Pythagorean Theorem

Answer 1

Cosine

Explanation:

There are 2 angles present and 1 length present, therefore you would use cosine.

Answer 2

To solve for
`a` tangent will be used because, tan theta equals to opposite side length divide by adjacent side length. Therefore, option C is correct

To solve for side
`\( a \)` in the right-angled triangle where
`\( a \)` is the side opposite the
`\( 43^\circ \)` angle, and the adjacent side is 11 units, we use the tangent function. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

The formula for tangent is:

`\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]`

Substituting the given values into the formula:

`\[\tan(43^\circ) = (a)/(11)\]`

To find
`a`, we rearrange the formula to solve for the opposite side:

`\[a = 11 * \tan(43^\circ)\]`

Using a calculator, we find that
`\( \tan(43^\circ) \)` is approximately
`\( 0.93251508613704 \)`. Multiplying this by the length of the adjacent side (11 units), we get:

`\[a \approx 11 * 0.93251508613704 \approx 10.26 \text{ units}\]`

Therefore, the length of side
`a` opposite the
`\( 43^\circ \)` angle is approximately
`\( 10.26 \)` units.