Question

etermining missing components of right triangles
use the information given in the diagram of △ghi to find the missing measurements. round all answers to the nearest tenth.
m∠g=
hi=
gh=

Explanation:

Step1: Find angle G

In a right - triangle, the sum of the interior angles is 180°. Given one angle is 90° and another is 30°.
$m\angle G=180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ}$

Step2: Find side HI

We know that $\sin G=\frac{HI}{GI}$. Given $GI = 30$ and $G = 60^{\circ}$.
$\sin60^{\circ}=\frac{HI}{30}$, so $HI = 30\times\sin60^{\circ}=30\times\frac{\sqrt{3}}{2}=15\sqrt{3}\approx26.0$

Step3: Find side GH

We know that $\cos G=\frac{GH}{GI}$. Given $GI = 30$ and $G = 60^{\circ}$.
$\cos60^{\circ}=\frac{GH}{30}$, so $GH = 30\times\cos60^{\circ}=30\times\frac{1}{2}=15$

Answer:

$m\angle G = 60^{\circ}$, $HI\approx26.0$, $GH = 15$