Question

Oh no! You have just discovered Superhero C is actually a villain! He plans toactivate an underwater volcano that is 50 miles away. Superhero A is goingto try to stop him.Suppose getting to the underwater volcano requires a combination ofrunning, flying, and swimming.Using the rates from Table 1, make a plan for how far each Superheroshould run, fly, and swim to make sure that Superhero A gets to the volcanobefore Superhero C and can save the world.Note: You must use all three modes of travel.

Answer 1

The missing leg of the triangle is 12 units long.

The degree measure of angle θ is approximately 21.8°.

The degree measure of angle φ is approximately 69.9°.

A right triangle with a hypotenuse and the length of one leg. We need to find the length of the other leg and the degree measure of the two non-right angles.

1. Identify the given information:

The hypotenuse of the triangle is labeled as 13 units.

The length of one leg is labeled as 5 units.

We need to find the length of the other leg (let's call it x) and the degree measures of the two non-right angles (let's call them θ and φ).

2. Use the Pythagorean theorem:

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. In this case, we can write the equation:

13² = 5² + x²

Solving for x, we get:

x² = 13² - 5²

x² = 144

x = √144

x = 12

Therefore, the length of the missing leg is 12 units.

3. Use trigonometric ratios to find the angles:

The sine (sin) function to find the measures of angles θ and φ. Remember that in a right triangle, the sine of an angle is equal to the opposite leg divided by the hypotenuse.

For angle θ:

sin(θ) = 5 / 13

θ ≈ 21.8°

For angle φ:

sin(φ) = 12 / 13

φ = arcsin(12 / 13)

φ ≈ 69.9°

Therefore, the degree measure of angle θ is approximately 21.8° and the degree measure of angle φ is approximately 69.9°.

Answer 2

First, let's calculate for superhero C the villian.

Using the three modes of travelling,

He needs to cover a distance of 50 miles

If he:

i. Runs

1 mile in 2 minutes, Hence

50 miles will be in 100 minutes

ii) Flys

2 miles in 2 minutes, Hence

50 miles will be in 50 minutes

iii) Swims

4 miles in 3 minutes, Hence

50 miles will be in 37.5 minutes

Next, let's calculate for superhero A.

Using the three modes of traveling,

He needs to cover a distance of 50 miles

If he:

i. Runs

4 miles in 1 minute, Hence

50 miles will be in 12.5 minutes

ii) Flys

4 miles in 4 minutes, Hence

50 miles will be in 50 minutes

iii) Swims

3 miles in 1 minute, Hence

50 miles will be in 16.67 minutes.

Finally, let's calculate for superhero B.

Using the three modes of traveling,

He needs to cover a distance of 50 miles

If he:

i. Runs

5 miles in 1 minute, Hence

50 miles will be in 10 minutes

ii) Flys

7 miles in 2 minutes, Hence

50 miles will be in 14.29 minutes

iii) Swims

10 miles in 3 minutes, Hence

50 miles will be in 15 minutes.