Question

Maria plans to make a triangular center island along the road. The said plan is illustrated at the image attached. She was able to put a fence around the lot which measures LT = 3m and OL = 3m. The said land area is an example of an oblique triangle which does not contain any right angle. If m∠T = 70 and m∠L = 65, what could be the measurement of ∠O and TO (round off to the nearest whole number)?

WITH SOLUTION!!!​

Answer 1

To find ∠O

The sum of interior angles of triangle sum up to 180°

Hence,

∠O + 70° + 65° = 180°

∠O = 180° - 65° - 70°

∠O = 45°

∴ The angle ∠O is 45 degrees.

To find length of TO

Use cosine rule: a² = b² + c² - 2bc cos(A)

Hence,

TO² = 3² + 3² - 2(3)(3) cos(65)

TO² = 10.39287129

To = √10.4

TO = 3.22 ≈ 3 meters (rounded to nearest whole number)

∴ The length of TO is 3 meters.