The diagram shows a 3 cm x 5 cm x 4 cm cuboid. a) Find length AC.
Give your answer to 2 decimal places.
b) Find angle ACD.
Give your answer to 1 decimal place.
D
4 cm
C
А
3 cm
5 cm
B

The side length AC is 5.83 cm and angle ACD is 34.5 degrees

(a) Length AC

To do this, we make use of the following Pythagoras theorem in triangle ABC

So, we have:

Take square roots

(b) Angle ACD

To do this, we make use of the following tangent ratio

So, we have:

Take arc tan of both sides

Hence, side length AC is 5.83 cm and angle ACD is 34.5 degrees

Read more about cuboids at:

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a) 5.83 cm

b) 34.4 deg

Step-by-step explanation:

a)

AC is the hypotenuse of a right triangle with legs measuring 3 cm and 5 cm.

c^2 = a^2 + b^2

c^2 = 3^2 + 5^2

c^2 = 9 + 25

c^2 = 34

c = sqrt(34) cm = 5.83 cm

b)

Triangle ACD is a right triangle with right angle DAC.

AD = 4 cm

AC = 5.83 cm

tan <ACD = opp/adj

tan <ACD = AD/AC

tan <ACD = 4/5.83

m<ACD = tan^-1 (0.68599)

m<ACD = 34.4 deg