Final answer:
To find the length of lp, we can use the properties of parallel and perpendicular lines. By using trigonometry and the given information, we can solve for lp.
Step-by-step explanation:
To solve for the length of lp, we can use the properties of parallel and perpendicular lines. First, we know that lm is parallel to kn. This means that the angles formed by them are congruent. Since m∠klm is given as 126°, we can use this angle to find m∠pkl and m∠lkn which are also 126°. Since lp is perpendicular to kn, m∠lpn must be 90°. Now, we can use trigonometry.
In triangle lpn, we have:
- ln = kn - lm = 30 - 20 = 10
- m∠lpn = 90°
- m∠nlm = m∠lpn - m∠klm = 90° - 126° = -36°
Using the cosine rule, we can find the length of lp:
lp² = ln² + lm² - 2(ln)(lm)cos(m∠nlm)
lp² = 10² + 20² - 2(10)(20)cos(-36°)
lp² = 100 + 400 - 400cos(36°)
lp² = 500 - 400(0.809)
lp² ≈ 197.84
lp ≈ √197.84
lp ≈ 14.05
So, the length of lp is approximately 14.05.