---I asked this question

Solve the following right triangles:
a. a=117 ft, b=16.35 ft
b. B=8 degrees 29',and a=32.8 ft

Reiny was kind enough to post this reply.

"solving" a triangle involves finding all missing sides and angles, so in
a) you found the sides, but still no angle.
tan B = 16.35/117 = 0.13974
angle B = 7.96°
subtract from 90° to find angle A

b) angle B = 8° 29' = (8+29/60)° = 8.48333°

tan 8.48333° = b/32.8
b= 4.892

now use Pythagoras to find the third side, and subtract angle B from 90 to get angle A

---but i am still having trouble with understanding the question and how the answers she posted were found .If u can explain to me in more details that would be great

The best tool to solve trigonometry and geometry problems is to draw a diagram. Unless you are very capable of drawing images in your mind, it is always a good idea to draw the figure, label it with all the given information and add more information as you go along.

This practice will not only help you solve the current problem, but you will, in time, see a pattern that will help you solve future problems.

Try to draw a right triangle, and label all the information on the figure. Proceed to solve as Reiny suggested. You will have no problem understanding Reiny's solution.

If you have problems creating the figures, see:

http://img823.imageshack.us/img823/6568/1295158166.jpg

There is a mistake in the figure for part a. TanB=... should read tan-1....

Sure, I'd be happy to explain the process in more detail.

In the problem given, we are asked to solve right triangles. To solve a right triangle means to find all the missing sides and angles.

a) In the first part of the problem, we are given the lengths of two sides, a and b. We want to find the missing angles.

To find angle B, we can use the tangent of the angle. The tangent of an angle is equal to the ratio of the side opposite the angle to the side adjacent to the angle. In this case, we can use tan B = b/a, where b is the side opposite angle B, and a is the side adjacent to angle B.

Using the given values a = 117 ft and b = 16.35 ft, we can find tan B = 16.35/117 = 0.13974. To find the angle B, we can take the inverse tangent of 0.13974, which gives us approximately 7.96 degrees.

Since this is a right triangle, the sum of the two angles must add up to 90 degrees. So to find angle A, we can subtract angle B from 90 degrees. In this case, angle A = 90 - 7.96 = 82.04 degrees.

b) In the second part of the problem, we are given the value of angle B and one side, a. We want to find the missing side length and angle.

First, we need to convert the angle B from degrees and minutes to decimal form. Since there are 60 minutes in a degree, we can convert the minutes to degrees by dividing by 60. In this case, 29 minutes is equal to 29/60 degrees. Adding this to the given 8 degrees, we get 8 + 29/60 = 8.48333 degrees.

Using the given value a = 32.8 ft and the angle B = 8.48333 degrees, we can use the tangent of the angle to find the missing side b. The formula tan B = b/a can be rearranged to b = a * tan B. Plugging in the values, we get b = 32.8 * tan(8.48333) ≈ 4.892 ft.

To find the third side, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we can use a^2 + b^2 = c^2, where c is the missing side. Plugging in the known values, we have 32.8^2 + 4.892^2 = c^2. Solving for c, we get c ≈ 33.37 ft.

Finally, we can find angle A by subtracting angle B from 90 degrees since it is a right triangle. In this case, angle A = 90 - 8.48333 ≈ 81.52 degrees.

I hope this explanation helps clarify the solution process for you. Let me know if you have any further questions!