Final answer:
The missing lengths AB and BC of a right-angled triangle with angle A at 60 degrees and hypotenuse AC at 10 units are found using trigonometric ratios; AB is approximately 8.66 units, and BC is exactly 5 units.
Step-by-step explanation:
To solve for the missing lengths AB and BC in a right-angled triangle, we can use trigonometric ratios and the Pythagorean theorem.
Given that angle A is 60 degrees and side AC (the hypotenuse in this case) is 10 units, we can find side AB (opposite to the 60-degree angle) using the sine function:
AB = AC × sin(60°)
Since sin(60°) is √3/2, we get:
AB = 10 x √3/2 ≈ 10 x 0.866 = 8.66 units (approximately).
To find side BC (adjacent to the 60-degree angle), we can use the cosine function:
BC = AC × cos(60°)
Since cos(60°) is 1/2, we get:
BC = 10 x 1/2 = 5 units.
Therefore, side AB is approximately 8.66 units, and side BC is exactly 5 units.
Find the missing lengths of sides AB and BC, we can use trigonometric ratios in a right-angled triangle. Given that angle A is 60 degrees, angle B is 45 degrees, and side AC is 10 units, let's find side AB and side BC.