Question

In ∆TUV, u = 5.2 cm, ZT=42º and ZU=56º. Find the length of t, to the nearest 10th of a centimeter.

a) 4.19
b) 4.2
c)-5.28
d)-5.3

Answer 1

To find the length of side t in triangle TUV, use the law of sines and angle measures to solve for t. The correct length of t is approximately 4.2 cm.

Step-by-step explanation:

The question asks us to find the length of side t in triangle TUV using the given measures of the other sides and angles. Since the angle measures given are ZT=42º and ZU=56º, we can find the third angle ZV using the fact that the sum of angles in a triangle is 180º. Therefore, ZV = 180º - 42º - 56º = 82º.

Using the law of sines, we have:

• sin(ZT) / t = sin(ZV) / u
• sin(42º) / t = sin(82º) / 5.2 cm

By cross-multiplication and solving for t we can calculate the length of side t.

Therefore, t = (sin(42º) / sin(82º)) * 5.2 cm, which calculates to approximately 4.2 cm, thus the answer 'b' is the correct choice.