Krishna
0

Step 1: Prove a similarity between the two triangles by using the theorems.

NOTE: The AA Similarity Theorem states that two triangles are similar if two angles of one triangle are congruent to

two angles of the other triangle.

EXAMPLE: \angle D = \angle G ( since angles with matching arcs are congruent.)

\angle E = \angle H = 90

Therefore, by the AA Similarity Theorem, △GHI~△DEF

Step 2: Find the unknown lengths of the triangle by using the similarity property.

NOTE: Ratios of corresponding side lengths are equal.

EXAMPLE: \frac{HI}{GI} = \frac{EF}{DF} ...............(1)

Step 3: Recall the sin definition.

DEFINITION: The sine (sin) of an angle in a right triangle is a ratio. It is the

length of the opposite leg (opp) divided by the length of the

hypotenuse (hyp).

EXAMPLE: \sin=\frac{opp}{hyp}=\frac{HI}{GI}

= \frac{EF}{DF}   [since equation(1)]

= \frac{48}{73}