Question

Pls help asap ty :))

Answer 1

`A \approx 33.203\textdegree`

`B \approx 73.398 \textdegree`

`C \approx 73.398\textdegree`

Explanation:

We can solve for the measures of ∠A, ∠B, and ∠C using the Law of Cosines, the Law of Sines, and the converse of the Isosceles Triangle Theorem.

First, plug the given a, b, and c lengths into the Law of Cosines to solve for the measure of angle A.

`a^2 = b^2 + c^2 - 2ab \cdot \cos(A)`

`a=4`,
`b=7`,
`c=7`

↓ plugging in for a, b, and c

`4^2 = 7^2 + 7^2 - 2(7)(7) \cdot \cos(A)`

↓ solving algebraically for cos(A)

`\cos(A) = (41)/(49)`

↓ taking inverse cosine of both sides

`A = \cos^(-1)\left((41)/(49)\right)`

↓ plugging into a calculator and rounding to three decimal places

`A \approx 33.203\textdegree`

Next, we can solve for the measure of angle B using the Law of Sines.

`(\sin(A))/(a) = (\sin(B))/(b)`

↓ plugging in A, a, and b

`(\sin(33.203\textdegree))/(4) = (\sin(B))/(7)`

↓ solving algebraically for sin(B)

`\sin(B) = (7)/(4)\sin(33.203\textdegree)`

↓ taking inverse sine of both sides

`B = \sin^(-1)\left((7)/(4)\sin(33.203\textdegree)\right)`

↓ plugging into a calculator and rounding to three decimal places

`B \approx 73.398 \textdegree`

Finally, we can solve for the measure of angle C using the converse of the Isosceles Triangle Theorem, which states that if two angles of a triangle are congruent, then the sides opposite those angles are also congruent.

`C = B`

`C \approx 73.398\textdegree`