Question

5. draw a picture of the scenario.6. find the degree measure of the angle of elevation between the location of the serpent princess in the search boat. show your work7. Solve for the rest of the missing side links in angle in the right triangle that represents this scenario. show your work and explain what each of these numbers represents in this context.

Answer 1

5. Let's make an illustration of the problem.

6. In order to find the degree measure of the angle of elevation between The Serpent Princess and the search boat, we can use the tangent function. The formula is:

`\theta=tan^(-1)\frac{opposite\text{ }side}{adjacent\text{ }side}`

Based on the illustration, with respect to the angle, its opposite side is 18 meters while its adjacent side is 50 meters. Let's put this into the formula above then, using a calculator, solve for the angle.

`\theta=tan^(-1)(18meters)/(50meters)\Rightarrow\theta=tan^(-1)(0.36)\Rightarrow\theta=19.7988\approx19.80\degree`

Therefore, the angle of elevation between The Serpent Princess and the search boat is approximately 19.80°.

7. Based on the illustration, the missing side is the distance between the search boat and The Serpent Princess. This is the hypotenuse of the right triangle in the illustration. We can solve this using the Pythagorean Theorem.

`c=√(a^2+b^2)`

where c = hypotenuse and "a" and "b" are the legs of the right triangle which is 18 meters and 50 meters.

Let's plug these values into the formula above.

`c=√(18^2+50^2)`

Then, solve.

`c=√(324+2500)\Rightarrow c=√(2824)\Rightarrow c\approx53.14meters`

The distance from the search boat to the Serpent Princess is approximately 53.14 meters.

Since the total measurement of the interior angles of a triangle is 180, to get the angle from The Howler to the search boat to The Serpent Princess, we can subtract the angle of elevation, 90° (right angle) from 180°.

`180-90-19.80=70.2`

Therefore, the angle from The Howler to the search boat to The Serpent Princess is 70.2°.

See the complete illustration with their sides and angles below.