New Zealand
Level 7 - NCEA Level 2

# Trigonometry in 3D

## Interactive practice questions

A square prism has sides of length $3$3cm, $3$3cm and $14$14cm as shown.

a

If the diagonal $HF$HF has a length of $z$z cm, calculate $z$z to two decimal places.

b

If the size of $\angle DFH$DFH is $\theta$θ°, find theta to two decimal places.

Easy
Approx 5 minutes

The following is a right pyramid on a square base with side length $12$12cm. A right pyramid has its apex aligned directly above the centre of its base.

The edge length $VA$VA is $23$23cm.

All edges of the following cube are $7$7 cm long.

A rectangular prism has dimensions as labelled on the diagram.

### Outcomes

#### M7-4

Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions

#### 91259

Apply trigonometric relationships in solving problems