Question

In stu, SU = 18 and TU = 13. Find mt to the nearest tenth of a degree.

a) 56.3 ∘

b) 64.1 ∘

c) 74.1∘

d) 81.8 ∘

Answer 1

To find mt, we can use the Law of Cosines and substitution. Simplify and solve for mt to find the approximate value of mt. The correct answer is b) 64.1°.

Step-by-step explanation:

To find mt, we need to use the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides and the cosine of the included angle. In this case, we have:

mt^2 = SU^2 + TU^2 - 2(SU)(TU)cos(mt)

Substituting the given values:

mt^2 = 18^2 + 13^2 - 2(18)(13)cos(mt)

Simplifying and solving for mt:

mt^2 = 324 + 169 - 468cos(mt)

mt^2 = 493 - 468cos(mt)

mt^2 + 468cos(mt) = 493

Now, we can use trial and error or a graphing calculator to find the approximate value of mt. By trying different values of mt, we can find that the answer closest to 0.1 would be approximately 64.1 degrees. Therefore, the correct answer is b) 64.1°.