Question

destiny is mountain climbing with troy and has just climbed a 15-meter vertical rock face. troy is standing 20 meters away from the bottom of the cliff, looking up at destiny. how far away are destiny and troy?
meters

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, where the vertical side (height Destiny climbed) is \(a = 15\) meters, the horizontal side (distance of Troy from the bottom) is \(b=20\) meters, and we need to find the hypotenuse \(c\) (distance between Destiny and Troy). We use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\).

Step2: Calculate \(a^{2}+b^{2}\)

First, calculate \(a^{2}\) and \(b^{2}\). \(a^{2}=15^{2}=225\) and \(b^{2}=20^{2} = 400\). Then \(a^{2}+b^{2}=225 + 400=625\).

Step3: Find the square root of the sum

Now, find \(c=\sqrt{625}\). Since \(25\times25 = 625\), \(\sqrt{625}=25\).

Answer:

25