For #2 use the Pythagorean Theorem:
a² + b² = c²
x² + 13² = 15²
x² = 15² - 13²
x² = 56 take the square root of both sides
x = √56 or 2√14
For # 4 Recognize that this is a special right triangle, 30-60-90 right triangle. As such, the ratios of the sides are 1:√3:2 This means if you know the shortest leg, you can multiply it by √3 to get the long leg, and you can find the hypotenuse by multiplying the short leg by 2.
Note: we are given the long leg of the right triangle, 12. So we know that the short leg, 'x', can be multiplied by √3 to get 12.
Or, we can write the equation: √3(x) = 12 and solve for 'x'
√3(x) = 12 divide both sides by √3
[tex]x= \frac{12}{ \sqrt{3} } [/tex] Rationalize the denominator
[tex]x=4 \sqrt{3} [/tex]
Now that we know the short leg, we can multiply it by 2 to get the hypotenuse, 'y'. y = [tex]8 \sqrt{3} [/tex]
