Question

question 25 (1 point) determine the length of the hypotenuse of the triangle to the nearest tenth of a metre. a) 2.1 m b) 3.1 m c) 2.9 m d) 2.4 m

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 55^{\circ}\), the opposite side is \(2.0\) m and the hypotenuse is \(h\). So, \(\sin(55^{\circ})=\frac{2.0}{h}\).

Step2: Solve for \(h\)

We can rewrite the equation as \(h=\frac{2.0}{\sin(55^{\circ})}\). Since \(\sin(55^{\circ})\approx0.8192\), then \(h=\frac{2.0}{0.8192}\approx2.44\approx2.4\) (rounded to the nearest tenth).

Answer:

d) \(2.4\) m