Question

find ( mangle x ).

(diagram of right triangle ( xvw ) with right angle at ( v ), ( xv = 2.8 ), ( xw = 3.5 ))

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle x approx square^circ )

Explanation:

Step1: Identify triangle type and sides

We have a right triangle \( \triangle XVW \) with right angle at \( V \). The adjacent side to \( \angle X \) is \( XV = 2.8 \), and the hypotenuse is \( XW = 3.5 \). We can use the cosine function, since \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \).
So, \( \cos(\angle X)=\frac{XV}{XW}=\frac{2.8}{3.5} \).

Step2: Calculate the cosine value

Simplify \( \frac{2.8}{3.5} = 0.8 \).

Step3: Find the angle

To find \( \angle X \), we take the inverse cosine (arccos) of \( 0.8 \). So, \( \angle X=\arccos(0.8) \). Using a calculator, \( \arccos(0.8)\approx36.9^\circ \) (rounded to the nearest tenth).

Answer:

\( 36.9 \)