Mathematics: (1) find mn to the nearest tenth (2) in triangle tuv below, find m !

(1) find mn to the nearest tenth (2) in triangle

Ответ:

RegencySlayer5304

04.01.2022

Mathematics

1. 64.0

2. 88°

Step-by-step explanation:

1. By the cosine rule,

$MN^2=NL^2+ML^2-2ML\cdot NL\cdot \cos\angle L,\\ \\MN^2=36^+47^2-2\cdot 36\cdot 47\cdot \cos 100^{\circ},\\ \\MN^2=1296+2209-3384\cos100^{\circ}\approx 4092.625433,\\ \\MN\approx 63.97\approx 64.0.$

2. Use the cosine rule,

$UV^2=UT^2+VT^2-2UT\cdot VT\cdot \angle T,\\ \\8.1^2=4.2^2+7.1^2-2\cdot 4.2\cdot 7.1\cdot \cos \angle T,\\ \\65.61=17.64+50.41-59.64\cos \angle T,\\ \\\cos \angle T=\dfrac{65.61-17.64-50.41}{-59.64}=\dfrac{2.44}{59.64}\approx 0.0409,\\ \\\angle T\approx 88^{\circ}.$