Question

Find the Tangent of ∠G.

image of a right triangle that has the following values, Angle G, Angle I, Angle H, Line GI which has an unknown length, Line IH which has a length of 12, and Line GH which has a length of 13

Answer 1

Since GH = 13 is the hypotenuse (13 is largest), the right angle is at I. Use the Pythagorean theorem to find GI:

GI^2 + IH^2 = GH^2
GI^2 + 12^2 = 13^2
GI^2 + 144 = 169
GI^2 = 25 → GI = 5

For angle G, opposite side = IH = 12 and adjacent = GI = 5, so

tan(G) = opposite/adjacent = 12/5 = 2.4.