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.

Question

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] · Answer 1 · 2022-04-07T06:54:27+03:00

IrinaVladis [17]3 years ago

5 0

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.....

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

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°