SOLUTION: I really need to answer these trigonometry problems. 1. The measure of two of the angles of a triangle are 50 degrees and 55 degrees. If its longest side measures 17 cm, find the

Question 389206: I really need to answer these trigonometry problems.
1. The measure of two of the angles of a triangle are 50 degrees and 55 degrees. If its longest side measures 17 cm, find the perimeter of the triangle.
2. The vertex angle of an isosceles triangle is 72 degrees and each of the equal sides is 10 cm. Find the perimeter and are of the triangle.
3. The diameter of a circle C is 34 cm. Two radii AC and BC from the angle of 96 degrees. Find the length of the cord AB.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I really need to answer these trigonometry problems.
1. The measure of two of the angles of a triangle are 50 degrees and 55 degrees. If its longest side measures 17 cm, find the perimeter of the triangle.
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The measure of the third angle is 180-(50+55) = 75 degrees
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Find the length of the side opposite the 50 degree angle.
Use the Law of Sines:
a/sin(50) = 17/sin(75)
---
a = sin(50)[17/sin(75)]
----
a = 13.48
==================
Find the length of the side opposite the 55 degree angle.
Use the Law of Sines:
b/sin(55) = [17/sin(75)]
b = sin(55)[17/sin(75)]
b = 14.42
=======================
Perimeter: 17 + 13.48 + 14.42
===================================
2. The vertex angle of an isosceles triangle is 72 degrees and each of the equal sides is 10 cm. Find the perimeter and area of the triangle.
---
Use the Law of Sines as in problem #1.
===================================
3. The diameter of a circle C is 34 cm. Two radii AC and BC form the angle of 96 degrees. Find the length of the cord AB.
---
Perimeter = (pi)d = 34pi
---
arc = (96/360)(34pi) = 28.48...cm
Cheers,
Stan H.

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