To find the measure of OT¯¯¯¯¯¯¯, we can use the law of cosines.
Let's define the third side of the triangle as OT⌢ = x units.
Using the law of cosines:
x^2 = 35.7^2 + OT^2 - 2(35.7)(OT)cos(146°)
Simplifying further:
x^2 = 1274.49 + OT^2 - 71.4OTcos(146°)
Since cos(146°) is a negative value, we can plug in the values and solve for x:
x^2 = 1274.49 + OT^2 + 71.4OT(0.766)
x^2 = 1274.49 + OT^2 - 54.611OT
Now we know that x = 35.7:
35.7^2 = 1274.49 + OT^2 - 54.611OT
1274.49 = 1274.49 + OT^2 - 54.611OT
0 = OT^2 - 54.611OT
Using the quadratic formula:
OT = (-(-54.611) ± √((-54.611)^2 - 4(1)(0))) / 2(1)
OT = (54.611 ± √(2986.619)) / 2
OT = (54.611 ± 54.619) / 2
OT = (109.23) / 2 or OT = (0.008) / 2
OT = 54.6155 or OT = 0.004
Since the length of a side of a triangle cannot be 0, we can discard the second solution, which leaves us with:
OT ≈ 55
Therefore, the measure of OT¯¯¯¯¯¯¯ is approximately 55 units.
f m∠COT=146∘
and CT⌢=35.7
units, what is the measure of OT¯¯¯¯¯¯¯?
Round your answer to the nearest whole number.
1 answer
1 answer