ABC is a right angled triangle .

AC= 16cm

Angle C = 90

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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.

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

A+B=90⇒ equation A

so

B=1.5A⇒ equation B

substitute equation B in equation A

A+1.5A=90

solve for A

step 2

Find the length of side AB (hypotenuse)

we know that

⇒ by CAH (adjacent side divided by the hypotenuse)

substitute the given values

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )