find vw. write your answer as an integer or as a decimal rounded to the nearest tenth. vw =
find vw. write your answer as an integer or as a decimal rounded to the nearest tenth. vw =
Answer
Explanation:
Step1: Identify the trig - ratio
In right - triangle $VWX$, we know the hypotenuse $VX = 9$ and we want to find the adjacent side $VW$ to the angle $\angle V=42^{\circ}$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. $\cos V=\frac{VW}{VX}$
Step2: Substitute the known values
We know that $V = 42^{\circ}$ and $VX = 9$. So, $\cos42^{\circ}=\frac{VW}{9}$. $VW = 9\times\cos42^{\circ}$
Step3: Calculate the value
Using a calculator, $\cos42^{\circ}\approx0.7431$. Then $VW = 9\times0.7431=6.6879$. Rounding to the nearest tenth, $VW\approx6.7$.
Answer:
$6.7$