Question

solve for x. round to the nearest tenth, if necessary.
(image of a right triangle abc with right angle at b, ab = 8, angle at c is 70 degrees, and bc = x)
answer attempt 1 out of 2
x = |

Explanation:

Step1: Identify triangle type

Triangle \(ABC\) is right - angled at \(B\), so we can use trigonometric ratios. We know the hypotenuse \(AC = 8\) and angle \(C=70^{\circ}\), and we want to find the length of side \(BC=x\) (adjacent to angle \(C\)).
The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 70^{\circ}\), adjacent side is \(x\), and hypotenuse is \(8\). So \(\cos(70^{\circ})=\frac{x}{8}\).

Step2: Solve for \(x\)

We can re - arrange the formula to solve for \(x\): \(x = 8\times\cos(70^{\circ})\).
We know that \(\cos(70^{\circ})\approx0.3420\). Then \(x=8\times0.3420 = 2.736\). Rounding to the nearest tenth, we get \(x\approx2.7\).

Answer:

\(2.7\)