Based on the diagram of the two right triangles, the measure of LK is equal to 3.6 units.
In order to determine the measure of LK, we would apply the tangent trigonometric function because the required and given side lengths represent the adjacent side and opposite side of a right-angled triangle respectively.
tan(θ) = Opp/Adj
Where:
- Adj represents the adjacent side of a right-angled triangle.
- Opp represents the opposite side of a right-angled triangle.
- θ represents the angle.
For this right-angled triangle KLM, we have the following equation for tanM:
tan(M°) = LK/MK
tan(24°) = LK/8
LK = 8 × tan(24°)
LK = 8 × 0.44522868530853616392236703064567
LK = 3.5618 ≈ 3.6 units.