Final answer:
The approximate height of an isosceles triangle with a 24-foot base and 63° base angles is around 23.55 feet. This is found using the tangent of one of the base angles and the length of half of the base.
Step-by-step explanation:
To find the approximate height (h) of an isosceles triangle with a base length of 24 feet and base angles of 63°, we will use trigonometric functions. Specifically, we can use the formula h = b * tan(\theta), where b is a base angle and \theta is the angle. Since it's an isosceles triangle, the two legs are congruent, and the height h will form two right triangles when drawn from the apex to the midpoint of the base.
First, we need to find the length of one of the legs of the right triangle by splitting the base into two equal parts of 12 feet. Next, we apply the tangent function:
- tan(63°) ≈ 1.9626
- h = 12 feet * 1.9626
- h ≈ 23.55 feet
Therefore, the approximate height of the isosceles triangle is 23.55 feet.