Question

practice 7 (from unit 4, lesson 7)
technology required. a rope with a length of 4 meters is tied from a stake in the ground to the top of a tent. it forms a 20° angle with the ground. how tall is the tent to the nearest tenth of a meter?
type your answer in the box.
_____ meters

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the rope is the hypotenuse (length \( c = 4 \) meters), the angle with the ground is \( \theta = 20^\circ \), and the height of the tent is the opposite side (\( h \)) to the angle. We use the sine function: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)

Step2: Solve for the height

Substitute the known values into the sine formula: \( \sin(20^\circ) = \frac{h}{4} \)
To find \( h \), multiply both sides by 4: \( h = 4 \times \sin(20^\circ) \)
Using a calculator, \( \sin(20^\circ) \approx 0.3420 \), so \( h \approx 4 \times 0.3420 = 1.368 \)

Step3: Round to the nearest tenth

Rounding \( 1.368 \) to the nearest tenth gives \( 1.4 \)

Answer:

1.4