Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
jk=

m∠j=

m∠k=

Explanation:

Step1: Find $JK$ (using Pythagorean theorem)

In right - triangle $\triangle IJK$, by the Pythagorean theorem $JK^{2}=IJ^{2}+IK^{2}$. Given $IJ = 10$ and $IK = 10$, then $JK^{2}=10^{2}+10^{2}=100 + 100=200$. So, $JK=\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}$.

Step2: Find $m\angle J$ and $m\angle K$

Since $\tan J=\frac{IK}{IJ}$, and $IK = IJ = 10$, then $\tan J=\frac{10}{10}=1$. We know that if $\tan\theta = 1$, then $\theta = 45^{\circ}$. Also, in a right - triangle $\triangle IJK$, $\angle I=90^{\circ}$, and $\angle J+\angle K = 90^{\circ}$. Since $\triangle IJK$ is an isosceles right - triangle ($IJ = IK$), $m\angle J=m\angle K$. So, $m\angle J = 45^{\circ}$ and $m\angle K = 45^{\circ}$.

Answer:

$JK = 10\sqrt{2}$; $m\angle J = 45^{\circ}$; $m\angle K = 45^{\circ}$