Answer:
∠A ≈ 66°
∠B ≈ 24°
AC ≈ 1.2
Step-by-step explanation:
SOH CAH TOA and the Pythagorean theorem are useful tools for solving right triangles. The first tells you ...
Sin = Opposite/Hypotenuse
For ∠A, that means ...
sin(A) = BC/AB = 2.7/2.95
The inverse sine function (sin⁻¹ or arcsin) is used to find the angle from its sine value, so ...
A = arcsin(2.7/2.95) ≈ 66°
Likewise, the ratio for angle B involves the adjacent side:
Cos = Adjacent/Hypotenuse
cos(B) = BC/AB = 2.7/2.95
B = arccos(2.7/2.95) ≈ 24°
Of course, angles A and B are complementary, so once you know angle A, you know that angle B is ...
∠B = 90° -∠A = 90° -66° = 24°
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The Pythagorean theorem can be used to find the unknown side. It tells you ...
AB² = AC² + BC²
2.95² = AC² + 2.7²
AC = √(2.95² -2.7²) ≈ 1.2
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These calculations are shown in the attachment using a TI-84 graphing calculator set to degrees mode. Any scientific or graphing calculator will do.
