Part 3/6:
Here, the tangent of the angle θ in the smaller triangle would be represented as a/2, while in the larger triangle it would be 4/2. By setting these equations equal, you could easily solve for 'a', identifying the length without extensive calculations.
Utilizing the Pythagorean Theorem
The discussion also highlighted a right-angle triangle scenario, where a height (H) needed to be determined. Given the base lengths of 20 and 15, the Pythagorean theorem could directly provide insights into finding H via the formula:
H² = 20² + 15².
However, direct evaluation may seem daunting without a calculator. Hence, an alternative method involves simplifying the triangle:
- Divide each side by a common factor, say 5.