Question

find the value of x, to the nearest tenth, in the triangle below. 6.1 8.7 7.1 9.5

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 35^{\circ}\), the opposite side is \(5\) and the hypotenuse is \(x\). So, \(\sin35^{\circ}=\frac{5}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x=\frac{5}{\sin35^{\circ}}\). We know that \(\sin35^{\circ}\approx0.5736\). Then \(x=\frac{5}{0.5736}\approx8.7\).

Answer:

\(8.7\)