Question

a graphic artist wants to make a triangle with a hypotenuse of 58 centimeters and a length of 42 centimeters. what will be the height of this triangle? select one of four 38 cm 40 cm 46 cm 60 cm remaining attempts: 1

Explanation:

Step1: Apply Pythagorean theorem

Let the height be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 58\) (hypotenuse) and \(a = 42\) (one side). So \(h=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 58\) and \(a = 42\) into the formula: \(h=\sqrt{58^{2}-42^{2}}=\sqrt{(58 + 42)(58 - 42)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
\(h=\sqrt{100\times16}\)

Step3: Calculate the result

\(\sqrt{100\times16}=\sqrt{100}\times\sqrt{16}=10\times4 = 40\)

Answer:

40 cm