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In the problem, angle c is a right angle. Solve the triangle rounding answers to the nearest tenth.c=13 in, m angle B= 35

User LoPiTaL
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1 Answer

20 votes
20 votes

Solve the following triangle

We are given two of the interior angles, c=90°, and b=35°. The third angle must have a measure such that the sum of them is 180°, thus:

a = 180° - 90° - 35° = 55°

Now calculate the length of BC by using the cosine ratio:


\cos 35^o=\frac{\text{adjacent side}}{hypotenuse}

Substituting;


\cos 35^o=(BC)/(13)

Solving for BC:

BC = 13 cos 35°

Calculating:

BC = 13 * 0.81915

BC = 10.6 in (to the nearest tenth)

For the length of AC, we use the sine ratio


\sin 35^o=\frac{\text{opposite side}}{hypotenuse}

Substituting:


\sin 35^o=(AC)/(13)

Solving for AC:

AC = 13 sin 35°

Calculating:

AC= 13 * 0.5736

AC = 7.4 in

Summary:

Angle A = 55°

Side BC = 10.6 in

Side AC = 7.4 in

In the problem, angle c is a right angle. Solve the triangle rounding answers to the-example-1
User Jacob Raccuia
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3.0k points