Question

find ( mangle t ).

write your answer as an integer or as a decimal rounded to the nearest tenth.

( mangle t=square^{circ} )

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(s^{2}=u^{2}+t^{2}-2ut\cos S\). For \(\triangle STU\), to find \(m\angle T\), we use the formula \(SU^{2}=ST^{2}+UT^{2}-2(ST)(UT)\cos T\). Let \(SU = 11\), \(ST = 12\), \(UT = 8\). Then \(11^{2}=12^{2}+8^{2}-2\times12\times8\times\cos T\).

$$121 = 144 + 64-192\cos T$$

$$121=208 - 192\cos T$$

$$192\cos T=208 - 121$$

$$192\cos T = 87$$

\(\cos T=\frac{87}{192}\approx0.453125\)

Step2: Find the angle \(T\)

Since \(\cos T\approx0.453125\), then \(T=\cos^{-1}(0.453125)\)
Using a calculator, \(T\approx63.1^{\circ}\)

Answer:

\(63.1\)