Question

a scalene triangle is shown below
what is the area of the obtuse triangle?
30 square centimeters
48 square centimeters
52 square centimeters
60 square centimeters

Explanation:

Step1: Find the height of the triangle

We use the sine function. For a right - triangle formed with the side of length \(15\) cm as the hypotenuse and the height \(h\) as the opposite side to the \(30^{\circ}\) angle.
The formula for sine is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Given \(\theta = 30^{\circ}\) and hypotenuse \(= 15\) cm.
So, \(h = 15\times\sin30^{\circ}\). Since \(\sin30^{\circ}=\frac{1}{2}\), then \(h = 15\times\frac{1}{2}=7.5\) cm.

Step2: Calculate the area of the triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). The base \(b = 8\) cm and height \(h = 7.5\) cm.
Substitute into the formula: \(A=\frac{1}{2}\times8\times7.5\).
First, \(8\times7.5 = 60\), then \(\frac{1}{2}\times60=30\) \(cm^{2}\).

Answer:

30 square centimeters