Question

ABC is a right angled triangle .

AC= 16cm

Angle C = 90......



Plz plz plz plz plz plz help

Answer 1

Answer:

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.

$AB=19.8\ cm$

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

$\frac{B}{A}=\frac{3}{2}$

so

B=1.5A⇒ equation B

substitute equation B in equation A

A+1.5A=90

solve for A

$2.5A=90\\A=36^o$

step 2

Find the length of side AB (hypotenuse)

we know that

$cos(A)=\frac{AC}{AB}$ ⇒ by CAH (adjacent side divided by the hypotenuse)

substitute the given values

$cos(36^o)=\frac{16}{AB}$

$AB=\frac{16}{cos(36^o)}=19.8\ cm$