Question

ok, heres another one (you can always go back a slide if you need to see the example again). given leg b=7 and hypotenuse c = 15, what is the length of leg a? answer this to one decimal place--rounded correctly--or it will be marked incorrect.

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right triangle is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. We need to solve for $a$, so rearrange the formula: $a^{2}=c^{2}-b^{2}$.

Step2: Substitute values

Given $b = 7$ and $c=15$, substitute into the formula: $a^{2}=15^{2}-7^{2}$. Calculate $15^{2}=225$ and $7^{2} = 49$, so $a^{2}=225 - 49=176$.

Step3: Solve for $a$

Take the square root of $176$: $a=\sqrt{176}$. Simplify $\sqrt{176}=\sqrt{16\times11}=4\sqrt{11}\approx4\times3.3166\approx13.3$ (rounded to one decimal place).

Answer:

13.3