Video: Finding the Cosine of Angles in Isosceles Triangles

Find the value of cos ๐ต.

01:28

Video Transcript

Find the value of cos ๐ต.

Looking at this triangle, thereโ€™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 ๐ด๐ท creates the height of the outer isosceles triangle. It also tells us something else. Line ๐ด๐ท creates a perpendicular line to line ๐ถ๐ต. And that means that it bisects line ๐ถ๐ต. Line ๐ถ๐ต can be broken up into two equal halves, both equal to 15 centimeters.

Cos of ๐ต can be found by looking at this interior right triangle. When weโ€™re dealing with right triangle trig, cos of ๐œƒ equals the adjacent side length over the hypotenuse side length. Cos of ๐ต must equal its adjacent side length, 15, over its hypotenuse side length, 34. Cos of angle ๐ต equals 15 over 34.

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