Question

question 27 (1 point) determine the length of the hypotenuse of the triangle to the nearest tenth of a metre. a) 2.9 m b) 2.1 m c) 2.4 m d) 3.1 m

Explanation:

Step1: Use sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 55^{\circ}\), and the length of the side opposite to the \(55^{\circ}\) angle is \(2.0\) m. Let the hypotenuse be \(h\). So, \(\sin55^{\circ}=\frac{2}{h}\).

Step2: Solve for \(h\)

We know that \(h=\frac{2}{\sin55^{\circ}}\). Since \(\sin55^{\circ}\approx0.8192\), then \(h=\frac{2}{0.8192}\approx2.4\)

Answer:

C. \(2.4\) m