Question

Could someone help me with this trigonometry question.

Answer 1

Answer:

About 75 degrees

Step-by-step explanation:

Let's call the point between C and B D. Using the Pythagorean Theorem, you know that CD is $\sqrt{112}$cm, meaning that BC has length $8+\sqrt{112}$cm. Additionally, we know that AB has length $\sqrt{208}$. Using the law of cosines:

$(8+\sqrt{112})^2=16^2+208-2(16)(\sqrt{208})\cdot \cos(A) \\\\345.328=256+208-461.511\cos(A) \\\\-461.511\cos(A)=-118.672 \\\\A=\cos^{-1}(0.2571)\approx 75^{\circ}$

Hope this helps!