Question

question 21
find the length of side x. round to the nearest tenth.
triangle with angles 45°, 75°, and side 9, side x
x =
question help:

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^\circ\). So the third angle \(A = 180^\circ - 75^\circ - 45^\circ = 60^\circ\).

Step2: Apply the Law of Sines

The Law of Sines states \(\frac{x}{\sin(45^\circ)}=\frac{9}{\sin(60^\circ)}\).
Solve for \(x\): \(x=\frac{9\times\sin(45^\circ)}{\sin(60^\circ)}\).
Calculate \(\sin(45^\circ)=\frac{\sqrt{2}}{2}\approx0.7071\), \(\sin(60^\circ)=\frac{\sqrt{3}}{2}\approx0.8660\).
Then \(x=\frac{9\times0.7071}{0.8660}\approx\frac{6.3639}{0.8660}\approx7.3\).

Answer:

\(7.3\)