Question

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.

Answer 1

Answer:

Step-by-step 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

$cosA=\frac{525}{600}$

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

$cosB=\frac{275}{400}$

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°