Question 468811
The altitude or height is always perpendicular to the opposite side.
Thus the altitude splits the triangle into 2 right triangles, of which the 2 hypotenuse sides are 70 and 90.
Let the vertices of one of the right triangles be ABC.
where AB = 70, BC = height
Using trig relationships:
sin(A) = height/70
=> height = 70*sin(A)
Now just find the measure of angle A by using the Law of Cosines:
90^2 = 70^2 + 80^2 - 2(70)(80)cos(A)
=> cos(A) = 0.2857
=> A = cos^-1(.2857) = 73.4
Substitute this value in for A to solve for height
=> height = 70*sin(73.4)
=> height = 67.1