Answer:
- AB ≈ 9.0 cm
- AC ≈ 10.0 cm
Explanation:
You want the side adjacent to a 29° angle in a right triangle with opposite side 5 cm. And you want the hypotenuse of a right triangle with the side opposite a 53.1° angle measuring 8 cm.
SOH CAH TOA
The mnemonic SOH CAH TOA is intended to remind you of the trig relations:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
Application
When working trig problems of this sort, you identify the sides of interest relative to the angle, then choose the relation that has those sides in it. As here, you may have to rearrange the equation to find the unknown value.
1. AB
The sides of interest are unknown leg AB adjacent to the angle, and marked side BC opposite the angle. These tell you that the tangent relation is of interest:
tan(29°) = BC/AB
AB = BC/tan(29°) = (5 cm)/tan(29°) ≈ 9.020 cm
The length of side AB is about 9.0 cm.
2. AC
The sides of interest are unknown hypotenuse AC and marked side CB opposite the angle. These tell you that the sine relation is of interest:
sin(53.1°) = CB/AC
AC = CB/sin(53.1°) = (8 cm)/sin(53.1°) ≈ 10.004 cm
The length of hypotenuse AC is about 10.0 cm.
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