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ABC is a right-angled triangle.
AC= 16cm
Angle c= 90• (degrees)
Size of angle b: size of angle A = 3:2
Work out the length of AB
Give your answer to 3 significant figures.

Respuesta :

calculista

Answer:

[tex]AB=19.8\ cm[/tex]

Step-by-step explanation:

step 1

Find the measure of angle A

we know that

Triangle ABC is a right triangle

so

The sum of angle A plus angle B must be equal to 90 degrees by complementary angles

[tex]A+B=90[/tex] ----> equation A

[tex]\frac{B}{A}=\frac{3}{2}[/tex]

so

[tex]B=1.5A[/tex] ----> equation B

substitute equation B in equation A

[tex]A+1.5A=90[/tex]

solve for A

[tex]2.5A=90\\A=36^o[/tex]

step 2

Find the length of side AB (hypotenuse)

we know that

[tex]cos(A)=\frac{AC}{AB}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(36^o)=\frac{16}{AB}[/tex]

[tex]AB=\frac{16}{cos(36^o)}=19.8\ cm[/tex]

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