In this page we practice solving different triangle problems using area formulas, the Pythagorean formula, and angle rules.
Example 1 – Area of a Right Triangle
\(\text{Base } = 1 \text{ m}\)
\(\text{Height} = 2 \text{ m}\)
$$\text{Area } = (1/2)(1)(2) = 1$$
\(\text{Area } = 1 \text{ m}^2\)
Example 2 – Area of an Obtuse Triangle
\(\text{Base } = 7 \text{ cm}\)
\(\text{Height} = 6 \text{ cm}\)
$$\text{Area } = (1/2)(7)(6) = 21$$
\(\text{Area } = 21 \text{ cm}^2\)
Example 3 – Area of an Acute Triangle
\(\text{Base } = 6\)
\(\text{Height} = 4\)
$$\text{Area } = (1/2)(6)(4) = 12$$
\(\text{Area } = 12 \text{ square units}\)
Example 4 – Pythagorean Formula
A right triangle has sides \(6\) and \(8\).
Find the hypotenuse.
\(x^2 = 6^2 + 8^2\)
\(x^2 = 36 + 64\)
\(x^2 = 100\)
\(x = 10\)
Example 5 – Finding a Missing Side
A right triangle has hypotenuse \(5\) and one side \(3\).
\(5^2 = x^2 + 3^2\)
\(25 = x^2 + 9\)
\(x^2 = 16\)
\(x = 4\)
Example 6 – Finding a Missing Interior Angle
Two angles are \(60^\circ\) and \(80^\circ\).
\(60^\circ + 80^\circ + x = 180\)
\(x = 40^\circ\)
Example 7 – Exterior Angles
Two exterior angles are \(120^\circ\) and \(120^\circ\).
\(120^\circ + 120^\circ + x = 360^\circ\)
\(x = 120^\circ\)
Practice
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