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Solve for all the missing angles for triangle ABC: a=10 cm, b=15 cm, c=20cm, state the angles in order (Angle A,B,C) and round answers to the nearest hundredth.

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6 votes

Answer:

Explanation:

This is not a right triangle, so that means we cannot use right triangle trig to solve. Since we have all the sides, we can, however, use the Law of Cosines. Let's first solve for angle A:


a^2=b^2+c^2-2bc(cosA)

Filling in:


10^2=15^2+20^2-2(15)(20)cosA and


100=225+400-600cosA and


100=625-600cosA and


-525=-600cosA and


cosA=(525)/(600)

Use the 2nd button then the cos button and enter in 525/600 to get the missing angle to be 28.96°

Do the same to find the measure of angle B:


15^2=10^2+20^2-2(10)(20)cosB and


225=100+400-400cosB and


225=500-400cosB and


-275=-400cosB and


cosB=(275)/(400)

Again, use the 2nd button and the cos button and enter 275/400 to get an angle measure of 46.57°

Now you can simply use the Triangle Angle-Sum Theorem to find angle C:

180 - 28.96 - 46.57 = 104.47°

To sum up, in order, Angle A = 28.96°, Angle B = 46.57°, Angle C = 104.47°

User Vinay Jeurkar
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