Question

solve the right triangle.
write your answers as integers or as decimals rounded to the nearest tenth.
$ik = $
$jk = $
$m\angle i = \quad ^\circ$
submit
work it out

Explanation:

Step1: Find $\angle I$

The sum of angles in a triangle is $180^\circ$. For right triangle $\triangle IJK$, $\angle J=90^\circ$, $\angle K=33^\circ$.
$m\angle I = 180^\circ - 90^\circ - 33^\circ = 57^\circ$

Step2: Calculate $JK$

Use tangent of $\angle K$: $\tan(K)=\frac{IJ}{JK}$
$\tan(33^\circ)=\frac{\sqrt{3}}{JK}$
$JK=\frac{\sqrt{3}}{\tan(33^\circ)}\approx\frac{1.732}{0.6494}\approx1.0$

Step3: Calculate $IK$

Use cosine of $\angle K$: $\cos(K)=\frac{JK}{IK}$
$\cos(33^\circ)=\frac{JK}{IK}$
$IK=\frac{JK}{\cos(33^\circ)}\approx\frac{1.0}{0.8387}\approx2.0$
Or use Pythagoras: $IK=\sqrt{IJ^2 + JK^2}=\sqrt{(\sqrt{3})^2 + 1^2}=\sqrt{3+1}=2.0$

Answer:

$IK = 2.0$, $JK = 1.0$, $m\angle I = 57.0^\circ$