In triangle DEF, the measure of angle E is 90°,
DE = 5, and DF= 13. The dimensions of DEF are
doubled to form triangle GHI with vertices D, E, and
F corresponding to vertices G, H, and I, respectively.
What is the value of tan I?

DF = 13; DE = 5 and EF = 12 using a²+ b² = c² meaning the squares of the two side of a right triangle = the square of the hypotenuse. EF = 12 because 5² + x² = 13² ; 25 + x² = 169 ; x² = 169 - 25 ; x² = 144 ; x = 12 .

Now GHI dimensions were doubled, so DE ≅ GH ; DF ≅ GI ; EF ≅ HI

So GH = 10; DF = 26; HI = 24.

Tan I = opposite /adjacent 10/24 = 5/12

In triangle DEF, the measure of angle E is 90°, DE = 5, and DF= 13. The dimensions of DEF are doubled to form triangle GHI with vertices D, E, and F corresponding to vertices G, H, and I, respectively. What is the value of tan I?

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In triangle DEF, the measure of angle E is 90°,
DE = 5, and DF= 13. The dimensions of DEF are
doubled to form triangle GHI with vertices D, E, and
F corresponding to vertices G, H, and I, respectively.
What is the value of tan I?