Trevor, robert, and maurice made some paper airplanes and want to see how far they will fly. the distance from trevor to robert is 13.5 feet. the distance from robert to maurice is 14.2 feet. the distance from maurice to trevor is 6.6 feet. find the measures of the three angles in the triangle.

a. m∠t=82.2, m∠r=27.4, m∠m=70.4

b. m∠t=27.4, m∠r=70.4, m∠m=82.2

c. m∠t=70.4, m∠r=82.2, m∠m=27.4

d. m∠t=60, m∠r=60, m∠m=60

a. m∠T=82.2, m∠R=27.4, m∠M=70.4

Step-by-step explanation:

Let T, R and M represent the position of Trevor, Robert, and Maurice respectively,

Given,

TR = 13.5 feet,

RM = 14.2 feet,

TM = 6.6 feet,

Since, TRM forms a triangle, ( because sum of any two sides is greater than third side )

By the law of cosine,

By substituting the values,

Similarly,

Hence, option 'a' is correct.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).