Question

partially correct (b) your answer is incorrect. for the right triangles below, find the exact values of the side lengths a and d. the figures are not drawn to scale. (a) a = \frac{\sqrt{2}}{2} (b) d = \frac{1}{2}

Explanation:

Step1: Solve for side length a

In a 45 - 45 - 90 right - triangle, the ratio of the side lengths is $1:1:\sqrt{2}$. If the hypotenuse $c = 1$, and the legs are of equal length $a$ and $b$. Using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, and since $a = b$, we have $2a^{2}=1$. Then $a^{2}=\frac{1}{2}$, so $a=\frac{\sqrt{2}}{2}$.

Step2: Solve for side length d

In a 30 - 60 - 90 right - triangle, the ratio of the side lengths is $1:\sqrt{3}:2$. If the hypotenuse $c = 1$ and the side opposite the 30 - degree angle is $d$. The side opposite the 30 - degree angle is half of the hypotenuse. So $d=\frac{1}{2}$.

Answer:

(a) $a=\frac{\sqrt{2}}{2}$
(b) $d = \frac{1}{2}$