Video: Finding the Cosine of Angles in Isosceles Triangles

Find the value of cos 𝐡.


Video Transcript

Find the value of cos 𝐡.

Looking at this triangle, there’s a few things we can note. The large triangle on the outside is an isosceles triangle, and both of the smaller interior triangles are right triangles. The line 𝐴𝐷 creates the height of the outer isosceles triangle. It also tells us something else. Line 𝐴𝐷 creates a perpendicular line to line 𝐢𝐡. And that means that it bisects line 𝐢𝐡. Line 𝐢𝐡 can be broken up into two equal halves, both equal to 15 centimeters.

Cos of 𝐡 can be found by looking at this interior right triangle. When we’re dealing with right triangle trig, cos of πœƒ equals the adjacent side length over the hypotenuse side length. Cos of 𝐡 must equal its adjacent side length, 15, over its hypotenuse side length, 34. Cos of angle 𝐡 equals 15 over 34.

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