Question

1. akiyo is designing a bird house with a symmetrical roof, as shown in the diagram. what is the total width of the bird house?

1. the statue of liberty is 305 ft tall, from the ground to the top of her torch. if you stood 115 ft away and used a clinometer to view the top of the statue, what would the clinometer read?

1. a guy wire that is used to support a pole is attached at a height of 72 ft and at an angle of 55.4° above the ground. how far from the base of the pole is the guy wire attached to the ground?

1. the scale factor for a model train is \\(\frac{1}{6}\\). if the actual train is 38 ft long, how long is the scale model?

1. a provincial flag measures 93 cm tall by 180 cm wide. if a replica pin is produced to scale, with a height of 1.4 cm, how wide would it be?

Explanation:

Solve for the half-width of the bird house

Using the Pythagorean Theorem knowledge point

$$
LATEXBLOCK0
$$

Calculate the total width of the bird house

Using the Geometric Decomposition knowledge point

$$ \text{Total Width} = 2x = 2 \times 11.00 = 22.0\text{ cm} $$

Determine the angle of elevation for the Statue of Liberty

Using the Right Triangle Trigonometry knowledge point

$$
LATEXBLOCK1
$$

Find the distance from the base of the pole to the guy wire

Using the Right Triangle Trigonometry knowledge point

$$
LATEXBLOCK2
$$

Calculate the length of the scale model train

We apply the given scale factor to the actual length:

$$ \text{Model Length} = 38\text{ ft} \times \frac{1}{6} \approx 6.33\text{ ft} $$

Calculate the width of the replica pin

We set up a proportion based on the scale ratio:

$$
LATEXBLOCK3
$$

Answer:

Question 21

The total width of the bird house is \(22.0\text{ cm}\).

Question 22

The clinometer would read approximately \(69.3^\circ\).

Question 23

The guy wire is attached approximately \(49.7\text{ ft}\) from the base of the pole.

Question 24

The scale model is approximately \(6.33\text{ ft}\) long (or \(6\frac{1}{3}\text{ ft}\)).

Question 25

The replica pin would be approximately \(2.71\text{ cm}\) wide.