Solve the following right triangles:
a. a=117 ft, b=16.35 ft
b. B=8 degrees 29',and a=32.8 ft
for a. got 118.14 by Applying the Pythagorean Theorem a^2 + b^2 = c^2.
can you show me the steps of how to solve b.
"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
Sure! To solve triangle b, we are given the measure of angle B and the length of side a.
Here are the steps to solve triangle b:
1. Start by labeling the triangle. Let's label the vertices as A, B, and C, and the sides opposite those vertices as a, b, and c respectively.
2. We are given that angle B measures 8 degrees 29'. To convert the minutes to degrees, we divide the given minutes (29') by 60, since there are 60 minutes in one degree. This gives us 29/60 = 0.4833 degrees.
3. Now, we can find the measure of angle C by subtracting the sum of angles A and B from 180 degrees. Since the sum of angles A and B is 180 degrees (as in any triangle), we have:
Angle C = 180 - 90 - (8 + 0.4833) = 180 - 98.4833 = 81.5167 degrees.
4. Next, we know the length of side a, which is given as 32.8 ft.
5. To find the length of side b, we can use the trigonometric ratio known as the sine function. In this case, the sine function relates the angle C to the ratio of the opposite side (b) to the hypotenuse (c). So we can write:
sin(C) = b/c
Rearranging the equation gives us:
b = c * sin(C)
6. To find the length of side c, we can use the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides (a and b) is equal to the square of the length of the longest side (c). Mathematically, we can express this as:
a^2 + b^2 = c^2
7. Now we can substitute the known values into the equation. We have:
32.8^2 + b^2 = c^2
8. Rearranging the equation and solving for b gives us:
b^2 = c^2 - 32.8^2
b = √(c^2 - 32.8^2)
9. Finally, we can substitute the value of b into the equation we derived earlier for b in terms of c and sin(C). So we have:
b = c * sin(C) = √(c^2 - 32.8^2)
With the value of b, we can solve for c by substituting the known values into the Pythagorean theorem equation:
32.8^2 + (√(c^2 - 32.8^2))^2 = c^2
Solving this equation will give us the length of side c and the approximate value of side b.
These are the steps to solve triangle b.