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 R=\angle W ( since angles with matching arcs are congruent.)

\angle S=\angle U=90

Therefore, by the AA Similarity Theorem, △RST ~ △WUV

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

NOTE: Ratios of corresponding side lengths are equal.

EXAMPLE: \frac{ST}{RS}=\frac{UV}{UW}...............(1)

Step 3: Recall the tan definition.

DEFINITION: The tangent (tan) of an angle in a right triangle is a ratio. It is the length of the oppositeleg (opp) divided by the length of the adjacent leg (adj).

EXAMPLE: \tan=\frac{opp}{adj}=\frac{ST}{RS}

= \frac{UV}{UW}  [since equation(1)]

= \tan\ R=\frac{20}{21}