Find altitude of isosceles triangle if angle=53 degrees (the equal angles) and the base is 8 inches.
To find the altitude of an isosceles triangle, you can use the trigonometric relationship between the angles and sides of a right triangle.
1. First, draw an isosceles triangle with the given information. Label the base as "b" (which is 8 inches in this case) and the equal sides as "a." Also, label the altitude as "h."
2. Since the triangle is isosceles, the angle opposite the base is also equal to the other two angles (53 degrees in this case).
3. Split the triangle into two right-angled triangles by drawing the altitude from the vertex of the triangle to the midpoint of the base. This will form two congruent right triangles.
4. Since we have split the triangle, each right-angled triangle will have an angle of 53 degrees.
5. Now, apply the trigonometric relationship for a right triangle. In this case, we can use the tangent function to relate the angle (53 degrees) and the sides of the triangle:
tan(53 degrees) = h / (b/2)
The length of h, which represents the altitude, is what we are trying to find.
6. Rearrange the equation to solve for h:
h = tan(53 degrees) * (b/2)
Substituting the given values, we get:
h = tan(53 degrees) * (8/2)
7. Evaluate the equation:
h = tan(53 degrees) * 4
Using a calculator, find the tangent of 53 degrees:
tan(53 degrees) ≈ 1.327
Substitute this value back into the equation:
h ≈ 1.327 * 4
h ≈ 5.308
Therefore, the altitude of the isosceles triangle is approximately 5.308 inches.