Question

Geometry homework help!! Please!!

Answer 1

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.