Question 1203384:
Found 3 solutions by josgarithmetic, Theo, ikleyn:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! This is quick but not complete...
b opposite point B
hypotenuse 5p, side a=70=4p
therefore p=35/2;
and solve for b, and solve for c and a.
.
.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! cos(b) = 4/5
a similar triangle would be those values multiplied by a common factor.
we'll call the common factor x.
you then get:
cos(B) = 4x/5x
you are given that a = 70
since a = 4x, this means that x = 70/4 = 17.5.
your common factor is 17.5
you have:
a = 70
c = 5 * 17.5 = 87.5
you can use pythagorus to get a^2 + b^2 = c^2 which becomes 70^2 + b^2 = 87.5^2.
solve for b^2 to get b^2 = 87.5^2 - 70^2 = 2756.25
solve for b to get b = square root of 2756.25 = 52.5
if you givide that by x = 17.5, you get b = 3.
you unit triangle is a 3,4,5 triangle.
b is equal to 3, a is equal to 4, c is equal to 5.
this is the triangle you get when the common factor is 1.
when you multiply by the common factor of 17.5, you get a 52.5, 70, 87.5 triangle.
the triangles are similar, which means the corresponding angles are congruent and the corresponding sides are proportional.
the triangle that i drew has A on the top left, B on the bottom right, and C on the bottom left.
a is the side opposite angle A, b ks the side opposite angle B, C is the side opposite angle C.
angle C is a right angle.
Answer by ikleyn(52908)  (Show Source):
|
|
|
