Questions: Solve the following triangles- Show all work for full credit. ( 5 marks each)

Solve the following triangles- Show all work for full credit. ( 5 marks each)
Transcript text: Solve the following triangles- Show all work for full credit. ( 5 marks each)
failed

Solution

failed
failed

Solution Steps

Step 1: Find Angle X

In triangle XYZ, angle Y is a right angle (90°). We are given that side XY = 5 and side YZ = 12. We can use the tangent function to find angle X. \\(\tan(X) = \frac{opposite}{adjacent} = \frac{12}{5} = 2.4\\) \\(X = \arctan(2.4) \approx 67.38°\\)

Step 2: Find Angle Z

The sum of the angles in a triangle is 180°. We know angle Y is 90° and angle X is approximately 67.38°. \\(Z = 180° - 90° - 67.38° \approx 22.62°\\)

Step 3: Find side z

We can use the Pythagorean theorem to find the length of side XZ (z). \\(z^2 = 5^2 + 12^2\\) \\(z^2 = 25 + 144\\) \\(z^2 = 169\\) \\(z = \sqrt{169} = 13\\)

Final Answer

\\( <X = \boxed{67.38°}\\) \\(<Z = \boxed{22.62°}\\) \\(Side \ z = \boxed{13}\\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
What is the variance and standard deviation of these groups of numbers? 24,67,17,20,31,44,12,23,16,37
failedAnswered
How much energy (in kJ) is required to raise the temperature of 219 g of water by 75.0°C?
failedAnswered
Let's eat: A fast-food restaurant chain has 604 outlets in the United States. The following table categorizes them by city population size and location, and presents the number of restaurants in each category. A restaurant is to be chosen at random from the 604 to test market a new menu. Round your answers to four decimal places. Population of City Region --- NE SE SW NW Under 50,000 - - - - 50,000-500,000 34 40 13 9 Over 500,000 56 88 70 33 (a) Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the Northeast? (b) Given that the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000? (c) Given that the restaurant is located in the Southwest, what is the probability that it is in a city with a population of 500,000 or less?
failedAnswered
Sole proprietorship Form 1120 Form 1120S Form 1065 Schedule C Partnership Match the business entity with the tax form used to report taxable income.
failedAnswered
The diaphragm separates the: mediastinum from the abdominal cavity. pelvic cavity from the abdominal cavity. pericardial cavity from the pleural cavity. mediastinum from the pleural cavity.