Triangle ABC solved: Angle A = 10.6°, side a = 0.749 cm, side b = 6.932 cm, side c = 7.022 cm.
Solving Right Triangle ABC
Sure, I can help you solve right triangle ABC with the given information. Here's how we can proceed:
1. Convert Angle:
First, let's convert the given angle from degrees and minutes to decimal degrees for easier calculations. We have:
A = 10° 36' = 10° + (36' / 60°) = 10.6° (rounded to three decimal places)
2. Identify Sides:
- `b` is given as 6.932 cm. We know this is the leg adjacent to angle A (opposite the right angle).
- We need to solve for the other leg (`a`) and the hypotenuse (`c`).
3. Use Trigonometric Ratios:
Since we have an angle and a side, we can use trigonometric ratios to solve for the missing parts. We have two options:
- Sine: We know the sine of angle A and the adjacent side (b). We can use the equation `sin(A) = a / c` to solve for `a`:
a = c * sin(A) = c * sin(10.6°) ≈ 0.121c
- Cosine: We know the cosine of angle A and the adjacent side (b). We can use the equation `cos(A) = b / c` to solve for `c`:
c = b / cos(A) = 6.932 cm / cos(10.6°) ≈ 7.022 cm
4. Solve for Remaining Side:
Now that we know one side (c), we can plug it back into the equation for the other side (a) to solve for it:
a = c * sin(A) ≈ 7.022 cm * sin(10.6°) ≈ 0.749 cm
Summary:
- Angle A = 10.6°
- Side a = 0.749 cm
- Side b = 6.932 cm
- Side c = 7.022 cm