Answer:
- A = 49
- B = 41
- C = 90
- a = 17.255526 (approximate)
- b = 15
- c = 22.863796 (approximate)
Round the decimal values however needed.
Explanation:
The uppercase letters represent the angles, while the lowercase counterparts are the side lengths opposite said angle. For example, side b is opposite angle B.
Angle B is 41 and angle C is 90 because of the square marker. The remaining angle A is...
A+B+C = 180
A+41+90 = 180
A+131 = 180
A = 180-131
A = 49
Or note that
A = 90 - B = 90 - 41 = 49
This shortcut works since we have a right triangle.
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That takes care of the angles. Now onto the sides.
We'll need to use trig ratios to determine the missing sides. There are a few approaches, but this is one you could take
tan(angle) = opposite/adjacent
tan(A) = a/b
tan(49) = a/15
a = 15*tan(49)
a = 17.255526 approximately
Furthermore,
sin(angle) = opposite/hypotenuse
sin(B) = b/c
sin(41) = 15/c
c*sin(41) = 15
c = 15/sin(41)
c = 22.863796 approximately
There is another trig function (cosine) that you could use. Also, you could use the pythagorean theorem once you know two sides of the right triangle.
The pythagorean theorem is a^2+b^2 = c^2
The answers have been confirmed with GeoGebra which is a useful geometry app.