Find altitude of isosceles triangle if è=53 degrees (the equal angles) and the base is 8 inches.
To find the altitude of an isosceles triangle, we need to use the properties of the triangle and apply trigonometry.
An isosceles triangle has two equal angles and two equal sides. In this case, the given equal angle is è (approximately 53 degrees). Let's call the base of the triangle "b" and the altitude "h."
To find the altitude, we can split the isosceles triangle into two right triangles by drawing a perpendicular line from the vertex angle (the angle opposite the base) to the center of the base. This perpendicular line represents the altitude.
Now, let's consider one of the right triangles formed by the base and the altitude. In this right triangle, the given angle is è/2 because it is half of the vertex angle. Therefore, the angle in this triangle is approximately 53 degrees / 2 = 26.5 degrees.
Using the trigonometric function tangent (tan), we can find the ratio of the opposite side (altitude, h) to the adjacent side (half of the base, b/2):
tan(26.5 degrees) = h / (b/2)
Since the base is given as 8 inches:
tan(26.5 degrees) = h / (8/2)
tan(26.5 degrees) = h / 4
To find the value of h, we rearrange the equation:
h = 4 * tan(26.5 degrees)
Now, we can calculate the value of h:
h ≈ 4 * tan(26.5 degrees)
h ≈ 4 * 0.5048
Calculating the above expression, we get:
h ≈ 2.0192 inches
Therefore, the altitude of the isosceles triangle is approximately 2.0192 inches.