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Chapter 8: Q. 5 (page 555)

In Problems 3–5, use the given information to determine the three remaining parts of each triangle.

Short Answer

Expert verified

The three angles of the triangle are∠A≈52.4°,∠B≈29.7°,and∠C≈97.9°.

Step by step solution

01

Step 1. Given Information

The sides of the triangle are AC=8,AB=10,andBC=8.

We have to determine the three remaining parts of the triangle which are three anglesA, B, and C.

02

Step 2. Finding ∠A

To find ∠A,we use the law of cosines formula which is role="math" localid="1647598615755" a2=b2+c2-2bccosA.

So,

82=52+102-2510cosA64-25-100=-100cosA-61-100=cosA0.61=cosAA=cos-10.61A≈52.4°

03

Step 3. Finding ∠B

To find ∠B,we use the law of cosines formula which is b2=a2+c2-2accosB.

So,

role="math" localid="1647599050264" 52=82+102-2810cosB25-64-100=-160cosB-139-160=cosB0.86875=cosBB=cos-10.86875B≈29.7°

04

Step 4. Finding ∠C

To find ∠C,we will use the sum of angles of a triangle which is 180°.

So,

∠A+∠B+∠C=180°52.4°+29.7°+∠C=180°∠C≈180°-82.1°∠C≈97.9°

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