a triangle has a base lenth of 8 and the length of the sides are both 10. it is divided by a bisector.?

Question

thus, forming two right triangles out of the triangle.what is the measurement of the bisector?

Answer 1

The bisector would form two right triangles with hypotnuse 10 an one side length 4. Using the pythagorean formula, a^2 + b^2 = c^2 you can solve for the missing side.
a^2 + 4^2 = 10^2
a^2 + 16 = 100
a^2 = 84
a= sqrt84

Answer 2

The original triangle is an isosceles triangle. Dropping a perpendicular bisector from the apex to the base gives you two right triangles with a hypotenuse of 10 and a short base of 4 (bisecting the base). Using the Pythagorean theorem;
a^2 + b^2 = c^2 where a = 4 and c = 10 gives you b.

Answer 3

Good old Pythagoras is the method. The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.... in mathematcs
c² = a² + b²

In your case
c² = a² + b²
10² = 4² + b²
100 = 16 + b²
100 - 16 = b²
84 = b²

Think you can take it from here? It's not going to be pretty... but it's not as bad a some you will run across in the future.

Answer 4

Yes, an isosceles triange's altitude, drawn from the unequal angle to the base is a bisector of that angle. It also bisects the base, so the right triangle will have one side of 4 and a length of 10. From Phythagorean Thm, the bisector has a length of sqrt(84) or 2sqrt(21)

Answer 5

both the right angled triangles have base of length 4
so from Pythagoras' theorem, base^2 + height^2 = hyp^2
so, here, 4^2 + height^2 = 10^2
so the bisector is = sqrt(100 - 16) = sqrt (84)