Question

1. 3 marks - 1, 2

farmer browns gate is beginning to sag and he decides to brace it be welding a steel bar across a diagonal. the gate is 4.20m long and 1.25m high.

a. draw a diagram to represent the dimensions given and the length of the brace.

b. how long will the brace need to be? give your answer to 1 decimal place.

Explanation:

Model the gate as a right triangle

Using the Right Triangle Modeling knowledge point

$$
LATEXBLOCK0
$$

Apply the Pythagorean theorem

Using the Pythagorean Theorem knowledge point

$$
LATEXBLOCK1
$$

Solve for the brace length

Using the Pythagorean Theorem knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question 9

a. A diagram representing the gate with a diagonal brace of length \(d\), height \(1.25\text{ m}\), and length \(4.20\text{ m}\) forming a right-angled triangle.

b. The brace will need to be \(4.4\text{ m}\) long.