Question

Triangle A B C. Angle C is 90 degrees. Hypotenuse side A B is c, C B is a, C A is b.

Solve the right triangle shown in the figure.
Side B C = 3.2 meters, angle B = 43.2 degrees, angle C = 90 degrees
a.
Angle A = 46.8 degrees, side A C = 1.9 meters, Side A B = 3.7 meters
c.
Angle A = 46.8 degrees, side A C = 5.3 meters, Side A B = 6.2 meters
b.
Angle A = 46.8 degrees, side A C = 5.3 meters, Side A B = 4.4 meters
d.
Angle A = 46.8 degrees, side A C = 3.0 meters, Side A B = 4.4 meters



Please select the best answer from the choices provided
see picture.......................

Answer 1

d. Angle A = 46.8 degrees, side AC = 3.0 meters, side AB = 4.4 meters

Explanation:

Given right triangle ABC and C = 90°, B = 43.2°, a = 3.2 m, you want the solution to the triangle.

Angle

The missing angle is found from ...

A = 180° -C -B = 180° -90° -43.2°

A = 46.8°

Sides

The given side is adjacent to the given acute angle, so the other two sides are ...

b = a·tan(B)

b = (3.2 m)·tan(43.2°) ≈ 3.0 m

and ...

c·cos(43.2°) = b

c = (3.2 m)/cos(43.2°) ≈ 4.4 m

The solution to the triangle is ...

A = 46.8°, b = 3.0 m, c = 4.4 m, matching choice D.

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