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Lelu [443]
3 years ago
13

What is m∠V ? Round only your final answer to the nearest tenth. 53.9º 56.1º 61.9º 70.0º The figure shows acute triangle U V W.

The length of side U V is 7.6 inches. The length of side V W is 8.6 inches. The length of side W U is 7.4 inches.

Mathematics
1 answer:
IrinaVladis [17]3 years ago
5 0

The correct option is:  53.9°

<em><u>Explanation</u></em>

According  to the below diagram,  \triangle UVW is acute triangle, in which \overline{UV}= 7.6 inches, \overline{VW}= 8.6 inches and \overline{WU}=7.4 inches

If we <u>apply cosine rule</u> here, then we will get.....

cos(V) = \frac{(UV)^2+(VW)^2 -(WU)^2}{2(UV)(VW)}

Now, plugging the given values, we will get....

cos(V)=\frac{(7.6)^2+(8.6)^2-(7.4)^2}{2(7.6)(8.6)}\\ \\ cos(V)= \frac{76.96}{130.72}=0.58873...\\ \\ V= cos^-^1(0.58873...)=53.932.... \approx 53.9 degree

So, the measure of \angle V is 53.9°


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