mimithurmond03

18.08.2021 •

Mathematics

Descreva a localização dos estabelecimentos abaixo utilizando termos com paralela transversal perpendicular

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Ответ:

juliannabartra

14.05.2022

Mathematics

AB= 20.9

$A = 33.2^\circ$

$C = 54.8^\circ$

Step-by-step explanation:

Given

The above triangle

Required

Complete the lengths

To do this, we make use of sine rule.

$\frac{a}{\sin A} = \frac{b}{\sin B}$

$\frac{14}{\sin A} = \frac{24}{\sin 70}$

$\frac{14}{\sin A} = 25.54$

Cross multiply

$\sin A * 25.54 = 14$

$\sin A = \frac{14}{25.54}$

$\sin A = 0.5482$

Take Arc sine of both sides

$A = sin^{-1}(0.5482)$

$A = 33.2^\circ$

To calculate C, we have:

C = 180 -A-B --- angles in a triangle

C = 180 -55.2-70

$C = 54.8^\circ$

Calculate length AB using the sine rule.

$\frac{AB}{sin C} = \frac{AC}{B}$

So, we have:

$\frac{AB}{sin 54.8} = \frac{24}{sin 70}$

Make AB the subject

$AB= sin 54.8*\frac{24}{sin 70}$

AB= sin 54.8* 25.54

AB= 20.9 -- approximated

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