Question

find uv.

u
√5
70°
w v

write your answer as an integer or as a decimal rounded to the nearest tenth.
uv =
submit

Explanation:

Step1: Identify triangle type and sides

Right triangle at U; UW = $\sqrt{5}$, ∠W=70°, UV is opposite ∠W.

Step2: Use tangent function

$\tan(70^\circ) = \frac{UV}{UW}$ → $UV = UW \cdot \tan(70^\circ)$

Step3: Calculate value

$UV = \sqrt{5} \cdot \tan(70^\circ) ≈ 2.236 \cdot 2.747 ≈ 6.14$? Wait correction: Wait UV is adjacent to ∠W? No, right triangle at U: sides - UW and UV are legs, WV hypotenuse. ∠W=70°, so opposite side to ∠W is UV, adjacent is UW. So $\tan(70) = UV/UW$ → UV = UW tan70 ≈ sqrt(5)2.747≈2.2362.747≈6.14? Wait no wait maybe I mixed: Wait no, if right angle at U, then ∠W=70°, so angle at W is 70°, so side opposite is UV, adjacent is UW. Yes. Wait sqrt(5)≈2.236, tan70≈2.747, product≈6.14→round to nearest tenth is 6.1? Wait wait no, wait maybe the side given is UW=√5, yes. So UV=√5 tan70≈6.1. Wait earlier miscalculation: 2.236*2.747≈6.14→6.1 when rounded to nearest tenth. Yes.

Wait correction on step3: $\sqrt{5}≈2.236$, $\tan(70^\circ)≈2.747$, so $2.236×2.747≈6.14≈6.1$.

Final answer 6.1.

Step1: Recognize right triangle parts

Right angle at U; UW=$\sqrt{5}$, ∠W=70°, UV opposite ∠W.

Step2: Apply tangent formula

$\tan(70^\circ)=\frac{UV}{UW}$ → $UV=UW·\tan(70^\circ)$

Step3: Compute numerical value

$UV≈\sqrt{5}×2.747≈2.236×2.747≈6.1$

Answer:

1.6