Answer:
- AC = 1.5 cm
- A = 61°
- B = 29°
Explanation:
You want the missing side and the angles for the right triangle with leg BC = 2.7 cm and hypotenuse AB = 3.1 cm.
Cosine
The cosine of angle B is given by ...
Cos = Adjacent/Hypotenuse
cos(B) = CB/AB = 2.7/3.1
Then the angle is ...
B = arccos(2.7/3.1) ≈ 29.429°
B ≈ 29°
Angle A is the complement of angle B:
A = 90° -29°
A = 61°
Sine
The sine ratio is ...
Sin = Opposite/Hypotenuse
Then side AC can be found from ...
sin(B) = AC/AB
AC = AB·sin(B) = 3.1·sin(29.429°) ≈ 1.523
AC ≈ 1.5 . . . . cm
The triangle solution is ...
- A = 61°
- B = 29°
- AC = 1.5 cm
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Additional comment
The mnemonic SOH CAH TOA is intended to help you remember the trig ratios above, in addition to ...
Tan = Opposite/Adjacent