When it comes to right triangles, there's one extremely important equation that you'll have to use almost every single time you come across one: the Pythagorean Theorem.
[tex]a^{2} + b^{2} = c^{2}[/tex]... Does that equation ring any bells? This equation is utilized to solve for any of the sides of a right triangle, given that you know the values of two of the sides. in a right triangle, there are three sides - one of which is known as a hypotenuse (the longest side of a right triangle). Variables a and b represent the lengths of the non-hypotenuse sides (basically, the two smaller sides, the ones that form a right angle). There's no special rule to which side is designated a and which is designated b, so don't worry about trying to figure out which side should be labeled which. Variable c represents the length of the hypotenuse.
Now, how can we apply the Pythagorean Theorem to this question? We are given the values of the two legs of the triangle, 1 m and [tex]\sqrt{15}[/tex] m. Since we are prompted to solve for the length of the hypotenuse, we will use the Pythagorean Theorem and solve for c, the variable for the length of the hypotenuse.
[tex]c^{2} = a^{2} + b^{2}[/tex]
c = [tex]\sqrt{a^{2} + b^{2} }[/tex]
(We square root both sides in order to isolate c. Now, let's plug in the values we were given. As we learned earlier, it doesn't matter which leg is a or b)
c = [tex]\sqrt{1^{2} + \sqrt{15}^{2} }[/tex]
c = [tex]\sqrt{1 + 15}[/tex]
c = [tex]\sqrt{16}[/tex]
c = 4 (m)
The length of the hypotenuse is 4 meters.
And we're done! Though I wrote a lot, the equation is fairly simple and will come extremely handy any time you're faced with questions like these. If you have any questions about anything I wrote here or you need clarification on anything, let me know!
- breezy ツ
