Question

The length of the base of an isosceles triangle is 30 m. The angle opposite to the base is 32 degrees. Find the perimeter of the triangle. Help?

Answer 1

Draw a triangle ABC as follows:-
Base is BC = 30
A = 32°
B = C = 74°

Sine Rule
30 / sin 32° = AC / sin 74°
AC = 30 sin 74° / sin 32°
AC = 54.4
AB = 54.4

P = 108.8 + 30 m
P = 138.8 m

<3Hope it helpssss

Answer 2

how did you get 74? :$

Answer 3

Drop a perpendicular from the 32 degree angle to the base. Now you have 2 triangles, each of which has angles of 16 degrees, 90 degrees and (by difference from 180) 74 degrees.

Cos 74 = .2756 = 15/x where x is one of the 2 equal legs of the isosceles triangle.

x = 54.427

Perimeter = 2 X 54.427 + 30 = 138.853

Answer 4

ohh why did you put 15/x? Other than that thank you so much! :)

Answer 5

x is one of the 2 equal legs of the isosceles triangle.
yourwel! :D

Answer 6

Consider the height as h, two equal sides as b and the base as a. Then use this formula -
h=sqrt(b^2-1/4a^2).

Answer 7

h = b*cos(1/2 of 32)
Let x be half of base (a) ie 30 = x = b*sin(1/2 of 32),
i.e h=b*cos16 and 30=b*sin16
Solve for b

Now perimeter is sum of all sides i.e a+2b i.e 30+2b