Question

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.

Answer 1

A. 53.9 degrees

Explanation:

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Answer 2

The correct option is: 53.9°

Explanation

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 apply cosine rule here, then we will get.....

`cos(V) = ((UV)^2+(VW)^2 -(WU)^2)/(2(UV)(VW))`

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

`cos(V)=((7.6)^2+(8.6)^2-(7.4)^2)/(2(7.6)(8.6))\\ \\ cos(V)= (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°