Question

17 multiple choice 2 points an isosceles triangle has a base with length 17 inches and two congruent sides with lengths of 15 inches each. find the height of the triangle. (round your answer to the nearest tenth of an inch.)

Explanation:

Step1: Divide the isosceles triangle

Divide the isosceles triangle into two right - angled triangles. The base of each right - angled triangle is \(b=\frac{17}{2} = 8.5\) inches, and the hypotenuse is \(c = 15\) inches. Let the height be \(h\).

Step2: Apply the Pythagorean theorem

According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), in our case \(h^{2}+b^{2}=c^{2}\), so \(h=\sqrt{c^{2}-b^{2}}\).
Substitute \(b = 8.5\) and \(c = 15\) into the formula:

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Answer:

\(12.4\) inches