Question

what would you use to solve for a? (triangle with right angle at c, side ac=11, angle at a=43°, side bc=a; options: tan, sin, pythagorean theorem, cos)

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$ (for sides $a,b$ and hypotenuse $c$ of a right - triangle).

Step2: Identify sides relative to the given angle

For angle $A = 43^{\circ}$, side $a$ (opposite to angle $A$) and side $11$ (adjacent to angle $A$) are known. Since we know the opposite and adjacent sides relative to the given angle, we use the tangent ratio. So, $\tan(A)=\frac{a}{11}$, and we can solve for $a$ as $a = 11\times\tan(43^{\circ})$.

Answer:

A. tan