Find the altitude of an isosceles triangle whose base is 8 cm and whose legs are 5 cm?
Since half of the isosceles would a right triangle, use the Pythagorean theorem with 1/2 value of the base.
4^2 + altitude^2 = 5^2
Solve for the altitude.
To find the altitude of an isosceles triangle, we can use the Pythagorean theorem.
Given that the base of the triangle is 8 cm and the legs are 5 cm, we can draw a perpendicular line from the top vertex to the base, dividing the base into two equal parts. This perpendicular line is the altitude we're looking for.
Let's call the altitude h.
Since the triangle is isosceles, the two base halves formed by the altitude are congruent right triangles.
Using the Pythagorean theorem, we can set up the equation as follows:
(5/2)^2 + h^2 = 5^2
Simplifying:
25/4 + h^2 = 25
Multiplying through by 4 to eliminate the fraction:
25 + 4h^2 = 100
Rearranging the equation:
4h^2 = 100 - 25
4h^2 = 75
Dividing both sides by 4:
h^2 = 75/4
Taking the square root of both sides to solve for h:
h = √(75/4) = √(75)/√(4) = (√(25) * √(3))/2 = (5 * √(3))/2
Therefore, the altitude of the isosceles triangle is (5 * √(3))/2 cm.
To find the altitude of an isosceles triangle, you can use the Pythagorean Theorem or trigonometric functions. Let's use the Pythagorean Theorem in this case.
Step 1: Draw the isosceles triangle with a base of 8 cm and legs of 5 cm each.
Step 2: Draw an altitude from the apex (top vertex) of the triangle to the base, creating two right triangles.
Step 3: The base of one of the right triangles is half the length of the base of the isosceles triangle, which is 8/2 = 4 cm.
Step 4: Apply the Pythagorean Theorem to find the altitude of one of the right triangles. The theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's call the altitude h, the base of the right triangle b, and the leg of the right triangle a. Using the Pythagorean Theorem, we have:
h^2 = a^2 - b^2
Since we know the base (b) is 4 cm and the leg (a) is 5 cm, we can substitute those values into the equation:
h^2 = 5^2 - 4^2
Simplifying:
h^2 = 25 - 16
h^2 = 9
Taking the square root of both sides, we find:
h = √9
h = 3
Therefore, the altitude of the isosceles triangle is 3 cm.