Question

ABCDEFGH is a cubiod

BH=26
BG=24

Work out the size of the angle HBG give your answer to 3 sf

Answer 1

The size of the angle is 48.2 degrees to 3 significant figures

The trigonometric functions are mathematical functions that establish relationships between an angle within a right-angled triangle and the ratios of its side lengths.

The trigonometric functions are defined as follows:

`\( sin(\theta) = \frac{{\text{opposite}}}{{\text{hypotenuse}}} \)\\\( cos(\theta) = \frac{{\text{adjacent}}}{{\text{hypotenuse}}} \)\\ \( tan(\theta) = \frac{{\text{opposite}}}{{\text{adjacent}}} \)`

In the context of a cuboid, consider Triangle BHG as a right triangle, where:

- BG = 24 cm (adjacent side)

- BH = 36 cm (opposite side)

Let's represent the angle HBG as x:

`\( cos(x) = \frac{{24}}{{36}} \)`

Solving for
`\( cos(x) \) gives \( cos(x) = 0.667 \)`, which corresponds to approximately

x = cos ⁻(0.667)

= 48.2 degrees