I have 2 problem that I don't know if I did it right. 1) right triangle with base=12 altitude=c, hypotenuse=d. 71 degrees is opposite 90 degrees. need to find C and d. I did tan 71=d/12. = 12 x 2.9042 = d = 34.85
Do I do the same process to get c?
2) right triangle with altitude=8, base=e, hypotenuse=f. 28 degree opposite 90 degree. I did sin28 deg= 8f/y= y=8/sin28 = y= 8/.4695. f=17.039 or 17. Again, do I do the same process for e?
in a triangle, angles are opposite sides. Two angles cannot be opposite each other.
Using the tan function, the hypotenuse is not used. If the base 12 is opposite the 71° angle, then
12/d = sin 71°
12/c = tan 71°
Better review your trig function definitions.
To solve these problems correctly, you need to use trigonometric ratios and the given information about the angles and sides of the right triangles. Let's go through each problem step by step.
Problem 1:
You have a right triangle with a base of 12 and an altitude of c, where the hypotenuse is d. The angle opposite the right angle (90 degrees) is 71 degrees.
To find d, you correctly used the tangent ratio: tan 71 = d/12.
However, the value of d you calculated (34.85) is incorrect. The correct calculation would be: d = 12 * tan 71 = 12 * 2.9042 = 34.85 (rounded to two decimal places).
Now, to find c, you can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides: c^2 + 12^2 = d^2.
Substituting the value obtained for d, you have: c^2 + 144 = (34.85)^2.
Simplifying the equation further: c^2 + 144 = 1212.1025.
Subtracting 144 from both sides: c^2 = 1212.1025 - 144 = 1068.1025.
Lastly, taking the square root of both sides: c = sqrt(1068.1025) ≈ 32.70 (rounded to two decimal places).
So, the correct values are d ≈ 34.85 and c ≈ 32.70.
Problem 2:
You have a right triangle with an altitude of 8, where the base is e and the hypotenuse is f. The angle opposite the right angle (90 degrees) is 28 degrees.
To find f, you correctly used the sine ratio: sin 28 = 8/f.
However, the value you calculated for f (17.039 or 17) is incorrect. The correct calculation would be: f = 8/sin 28 ≈ 17.01 (rounded to two decimal places).
To find e, you can again use the Pythagorean theorem: e^2 + 8^2 = f^2.
Substituting the value we obtained for f, you have: e^2 + 64 = (17.01)^2.
Simplifying the equation further: e^2 + 64 = 289.1401.
Subtracting 64 from both sides: e^2 = 289.1401 - 64 = 225.1401.
Taking the square root of both sides: e = sqrt(225.1401) ≈ 15 (rounded to two decimal places).
So, the correct values are f ≈ 17.01 and e ≈ 15.
In summary, for both problems, you used the correct trigonometric ratios but made errors in your calculations, resulting in incorrect answers. By following the correct steps explained above, you will find the accurate solutions.