How do you find the angles of a triangle given side a = 10, side b = 10, base = 15?

1 Answer
Sep 17, 2016

see below.

Explanation:

Given is that 2 sides are of same length i.e. 10cm. This tells us that this is an isosceles triangle.

{ Isosceles triangles have 2 same angles and one different angle .}

enter image source here

so using above picture let AC and BC be 10cm. And AB be 15 cm.

Now find CD using Pythagoras theorem, {then later the angle will be found}

10^2=7.5^2+CD^2 {7.5 is half of 15 i.e length DB}

CD^2=10^2-7.5^2

CD=6.6

Now apply trigonometric ratio(s)

tan B = (CD)/(BD)

tanB=6.6/7.5

B=tan^-1(6.6/7.5)

B=41.34

Hence color(red)"angle B is 41.34 degrees" .

Therefore color(blue)("angle A will also be 41.34 degrees.")

Now its simple,

180^o=41.34^o + 41.34^o +/_C

/_C=180^o-41.34^o-41.34^o

/_C=97.32^o

hence color(green)"angle C is 97.32 degrees"