Question

consider right triangle $\triangle ghi$ below.

which expressions represent the length of side $\overline{hi}$?
choose 2 answers:
a $8.3 \cdot \sin(90^{\circ} - 75^{\circ})$
b $8.3 \cdot \cos(90^{\circ} - 75^{\circ})$
c $8 \cdot \tan(90^{\circ} - 75^{\circ})$
d $\frac{8}{\tan(90^{\circ} - 75^{\circ})}$

Explanation:

Step1: Identify angle at G

First, calculate $\angle G$:
$\angle G = 90^\circ - 75^\circ = 15^\circ$

Step2: Use sine for $\triangle GHI$

In right $\triangle GHI$, $\sin(\angle G) = \frac{\overline{HI}}{\overline{GH}}$. Rearranged:
$\overline{HI} = 8.3 \cdot \sin(90^\circ - 75^\circ)$

Step3: Use tangent for $\triangle GHI$

Also, $\tan(\angle G) = \frac{\overline{HI}}{\overline{GI}}$, so rearranged:
$\overline{HI} = 8 \cdot \tan(90^\circ - 75^\circ)$

Answer:

A. $8.3 \cdot \sin(90^\circ - 75^\circ)$
C. $8 \cdot \tan(90^\circ - 75^\circ)$