Question

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​

Answer 1

Answer:

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

Answer 2

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

$\mathbf{AC^2 = AB^2 + BC^2}$

So, we have:

$\mathbf{AC^2 = 3^2 + 5^2}$

$\mathbf{AC^2 = 9 + 25}$

$\mathbf{AC^2 = 34}$

Take square roots

$\mathbf{AC = 5.83}$

(b) Angle ACD

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

$\mathbf{tan(C) = \frac{AD}{AC}}$

So, we have:

$\mathbf{tan(C) = \frac{4}{5.83}}$

$\mathbf{tan(C) = 0.6861}$

Take arc tan of both sides

$\mathbf{C= 34.5}$

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

Read more about cuboids at:

https://brainly.com/question/19810528