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In triangle ABC, AC = 13 cm, angle A = 4y - 71°, angle B = y + 7°, and angle C = 106 - 2y°. In triangle RST,

RT = 2x + 5 cm and angle R = 113°. Angle B is congruent to Angle S
and segment AB is congruent to segment RS.

User LaptopHeaven
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1 Answer

25 votes
25 votes

Answer:

The length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.

Explanation:

Since angle A and angle R are both congruent to angle B, we know that angle A = angle R = y + 7°. We can use this information, along with the angles and sides of the triangles, to find the value of y and the lengths of the sides of the triangles.

From the given information, we know that the angles of triangle ABC add up to 180°, so we can use that to find the value of y:

4y - 71° + y + 7° + 106 - 2y° = 180°

6y - 64° = 180°

6y = 244°

y = 40.67°

We can use the value of y to find the measure of angle C:

C = 106 - 2y° = 106 - 2(40.67°) = 106 - 81.34° = 24.66°

Now that we know the measure of angle C, we can use the Law of Sines to find the length of side BC:

BC / sin C = AC / sin A

BC = (AC * sin C) / sin A

BC = (13 cm * sin 24.66°) / sin (4y - 71°)

BC = (13 cm * 0.4237) / sin (4(40.67°) - 71°)

BC = 5.525 cm

We can use the same method to find the length of side ST in triangle RST:

ST = (RT * sin C) / sin A

ST = ((2x + 5 cm) * sin 24.66°) / sin (4y - 71°)

ST = ((2x + 5 cm) * 0.4237) / sin (4(40.67°) - 71°)

ST = (2x + 5 cm) * 0.4237 * 0.4514

ST = (2x + 5 cm) * 0.1901

ST = 0.3802x + 0.9505 cm

Therefore, the length of side BC in triangle ABC is 5.525 cm, and the length of side ST in triangle RST is 0.3802x + 0.9505 cm.

User MaicolBen
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