Question

Here is a cuboid.

H Н.
G
31.5 cm
E
F
с
36 cm
А
27 cm
B
Calculate the size of angle CAG.

Answer 1

To calculate the size of angle CAG in the given cuboid, we need to analyze the dimensions and use trigonometric ratios. Using the lengths of AG, AC, and CG, we can determine the size of angle CAG to be approximately 40.8 degrees.

Step-by-step explanation:

To calculate the size of angle CAG, we need to analyze the given cuboid diagram. Angle CAG is located at the top corner of the cuboid, where the edges AG and AC meet. To determine the size of angle CAG, we need to consider the dimensions of the cuboid and use trigonometric ratios.

From the given diagram, we can see that AG has a length of 31.5 cm, AC has a length of 27 cm, and CG has a length of 36 cm. Using these measurements, we can apply the trigonometric ratio:

• Tan(CAG) = AC/AG
• Tan(CAG) = 27/31.5
• Tan(CAG) = 0.857

Using the inverse tangent function on a calculator, we find that CAG ≈ 40.8°. Therefore, the size of angle CAG in the given cuboid is approximately 40.8 degrees.

Answer 2

m(∠CAG) = 35°

Step-by-step explanation:

From the figure attached,

Apply Pythagoras theorem in ΔCAG,

Length of AC =
`√((27)^2+(36)^2)`

=
`√(729+1296)`

=
`√(2025)`

= 45

Now find the tangent of the given angle CAG,

tan(∠CAG) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

=
`(CG)/(AC)`

m(∠CAG) =
`\text{tan}^(-1)((31.5)/(45) )`

=
`\text{tan}^(-1)(0.7)`

= 34.992°

≈ 35°